Find the Function Rule table[[x,y],[-1,-9],[0,-5],[1,-1],[2,-1]]

Math
xy-1-90-51-12-1
Check if the function rule is linear.
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To find if the table follows a function rule, check to see if the values follow the linear form y=ax+b.
y=ax+b
Build a set of equations from the table such that y=ax+b.
-9=a(-1)+b-5=a(0)+b-1=a(1)+b-1=a(2)+b
Calculate the values of a and b.
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Simplify each equation.
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Simplify a(0)+b.
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Multiply a by 0.
-5=0+b
-9=a(-1)+b
-1=a(1)+b
-1=a(2)+b
Add 0 and b.
-5=b
-9=a(-1)+b
-1=a(1)+b
-1=a(2)+b
-5=b
-9=a(-1)+b
-1=a(1)+b
-1=a(2)+b
Simplify each term.
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Move -1 to the left of a.
-5=b
-9=-1⋅a+b
-1=a(1)+b
-1=a(2)+b
Rewrite -1a as -a.
-5=b
-9=-a+b
-1=a(1)+b
-1=a(2)+b
-5=b
-9=-a+b
-1=a(1)+b
-1=a(2)+b
Multiply a by 1.
-5=b
-9=-a+b
-1=a+b
-1=a(2)+b
Move 2 to the left of a.
-5=b
-9=-a+b
-1=a+b
-1=2a+b
-5=b
-9=-a+b
-1=a+b
-1=2a+b
Rewrite the equation as b=-5.
b=-5
-9=-a+b
-1=a+b
-1=2a+b
Replace all occurrences of b with -5 in each equation.
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Replace all occurrences of b in -9=-a+b with -5.
b=-5
-9=-a-5
-1=a+b
-1=2a+b
Replace all occurrences of b in -1=a+b with -5.
b=-5
-9=-a-5
-1=a-5
-1=2a+b
Replace all occurrences of b in -1=2a+b with -5.
b=-5
-9=-a-5
-1=a-5
-1=2a-5
b=-5
-9=-a-5
-1=a-5
-1=2a-5
Simplify.
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Remove parentheses.
b=-5
-9=-a-5
-1=a-5
-1=2a-5
Remove parentheses.
b=-5
-9=-a-5
-1=a-5
-1=2a-5
Remove parentheses.
b=-5
-9=-a-5
-1=a-5
-1=2a-5
b=-5
-9=-a-5
-1=a-5
-1=2a-5
Solve for a in the second equation.
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Rewrite the equation as -a-5=-9.
b=-5
-a-5=-9
-1=a-5
-1=2a-5
Move all terms not containing a to the right side of the equation.
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Add 5 to both sides of the equation.
b=-5
-a=-9+5
-1=a-5
-1=2a-5
Add -9 and 5.
b=-5
-a=-4
-1=a-5
-1=2a-5
b=-5
-a=-4
-1=a-5
-1=2a-5
Multiply each term in -a=-4 by -1
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Multiply each term in -a=-4 by -1.
b=-5
(-a)⋅-1=(-4)⋅-1
-1=a-5
-1=2a-5
Multiply (-a)⋅-1.
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Multiply -1 by -1.
b=-5
1a=(-4)⋅-1
-1=a-5
-1=2a-5
Multiply a by 1.
b=-5
a=(-4)⋅-1
-1=a-5
-1=2a-5
b=-5
a=(-4)⋅-1
-1=a-5
-1=2a-5
Multiply -4 by -1.
b=-5
a=4
-1=a-5
-1=2a-5
b=-5
a=4
-1=a-5
-1=2a-5
b=-5
a=4
-1=a-5
-1=2a-5
Replace all occurrences of a with 4 in each equation.
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Replace all occurrences of a in -1=a-5 with 4.
b=-5
a=4
-1=(4)-5
-1=2a-5
Replace all occurrences of a in -1=2a-5 with 4.
b=-5
a=4
-1=(4)-5
-1=2(4)-5
b=-5
a=4
-1=(4)-5
-1=2(4)-5
Simplify.
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Subtract 5 from 4.
b=-5
a=4
-1=-1
-1=2(4)-5
Simplify 2(4)-5.
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Multiply 2 by 4.
b=-5
a=4
-1=-1
-1=8-5
Subtract 5 from 8.
b=-5
a=4
-1=-1
-1=3
b=-5
a=4
-1=-1
-1=3
b=-5
a=4
-1=-1
-1=3
Since -1=-1, the equation will always be true.
b=-5
a=4
Always true
-1=3
Remove any equations from the system that are always true.
b=-5
a=4
-1=3
Since -1≠3, there are no solutions.
b=-5
a=4
Always true
No solution
Remove any equations from the system that are always true.
b=-5
a=4
No solution
b=-5
a=4
No solution
Calculate the value of y using each x value in the relation and compare this value to the given y value in the relation.
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Calculate the value of y when a=4, b=-5, and x=-1.
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Multiply 4 by -1.
y=-4-5
Subtract 5 from -4.
y=-9
y=-9
If the table has a linear function rule, y=y for the corresponding x value, x=-1. This check passes since y=-9 and y=-9.
-9=-9
Calculate the value of y when a=4, b=-5, and x=0.
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Multiply 4 by 0.
y=0-5
Subtract 5 from 0.
y=-5
y=-5
If the table has a linear function rule, y=y for the corresponding x value, x=0. This check passes since y=-5 and y=-5.
-5=-5
Calculate the value of y when a=4, b=-5, and x=1.
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Multiply 4 by 1.
y=4-5
Subtract 5 from 4.
y=-1
y=-1
If the table has a linear function rule, y=y for the corresponding x value, x=1. This check passes since y=-1 and y=-1.
-1=-1
Calculate the value of y when a=4, b=-5, and x=2.
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Multiply 4 by 2.
y=8-5
Subtract 5 from 8.
y=3
y=3
If the table has a linear function rule, y=y for the corresponding x value, x=2. This check does not pass, since y=3 and y=-1. The function rule can’t be linear.
3≠-1
Since y≠y for the corresponding x values, the function is not linear.
The function is not linear
The function is not linear
The function is not linear
Check if the function rule is quadratic.
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To find if the table follows a function rule, check whether the function rule could follow the form y=ax2+bx+c.
y=ax2+bx+c
Build a set of 3 equations from the table such that y=ax2+bx+c.
Calculate the values of a, b, and c.
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Simplify each equation.
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Simplify a(0)2+b(0)+c.
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Simplify each term.
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Raising 0 to any positive power yields 0.
-5=a⋅0+b(0)+c
-9=a(-1)2+b(-1)+c
-1=a(1)2+b(1)+c
-1=a(2)2+b(2)+c
Multiply a by 0.
-5=0+b(0)+c
-9=a(-1)2+b(-1)+c
-1=a(1)2+b(1)+c
-1=a(2)2+b(2)+c
Multiply b by 0.
-5=0+0+c
-9=a(-1)2+b(-1)+c
-1=a(1)2+b(1)+c
-1=a(2)2+b(2)+c
-5=0+0+c
-9=a(-1)2+b(-1)+c
-1=a(1)2+b(1)+c
-1=a(2)2+b(2)+c
Combine the opposite terms in 0+0+c.
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Add 0 and 0.
-5=0+c
-9=a(-1)2+b(-1)+c
-1=a(1)2+b(1)+c
-1=a(2)2+b(2)+c
Add 0 and c.
-5=c
-9=a(-1)2+b(-1)+c
-1=a(1)2+b(1)+c
-1=a(2)2+b(2)+c
-5=c
-9=a(-1)2+b(-1)+c
-1=a(1)2+b(1)+c
-1=a(2)2+b(2)+c
-5=c
-9=a(-1)2+b(-1)+c
-1=a(1)2+b(1)+c
-1=a(2)2+b(2)+c
Simplify each term.
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Raise -1 to the power of 2.
-5=c
-9=a⋅1+b(-1)+c
-1=a(1)2+b(1)+c
-1=a(2)2+b(2)+c
Multiply a by 1.
-5=c
-9=a+b(-1)+c
-1=a(1)2+b(1)+c
-1=a(2)2+b(2)+c
Move -1 to the left of b.
-5=c
-9=a-1⋅b+c
-1=a(1)2+b(1)+c
-1=a(2)2+b(2)+c
Rewrite -1b as -b.
-5=c
-9=a-b+c
-1=a(1)2+b(1)+c
-1=a(2)2+b(2)+c
-5=c
-9=a-b+c
-1=a(1)2+b(1)+c
-1=a(2)2+b(2)+c
Simplify each term.
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One to any power is one.
-5=c
-9=a-b+c
-1=a⋅1+b(1)+c
-1=a(2)2+b(2)+c
Multiply a by 1.
-5=c
-9=a-b+c
-1=a+b(1)+c
-1=a(2)2+b(2)+c
Multiply b by 1.
-5=c
-9=a-b+c
-1=a+b+c
-1=a(2)2+b(2)+c
-5=c
-9=a-b+c
-1=a+b+c
-1=a(2)2+b(2)+c
Simplify each term.
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Raise 2 to the power of 2.
-5=c
-9=a-b+c
-1=a+b+c
-1=a⋅4+b(2)+c
Move 4 to the left of a.
-5=c
-9=a-b+c
-1=a+b+c
-1=4⋅a+b(2)+c
Move 2 to the left of b.
-5=c
-9=a-b+c
-1=a+b+c
-1=4a+2b+c
-5=c
-9=a-b+c
-1=a+b+c
-1=4a+2b+c
-5=c
-9=a-b+c
-1=a+b+c
-1=4a+2b+c
Rewrite the equation as c=-5.
c=-5
-9=a-b+c
-1=a+b+c
-1=4a+2b+c
Replace all occurrences of c with -5 in each equation.
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Replace all occurrences of c in -9=a-b+c with -5.
c=-5
-9=a-b-5
-1=a+b+c
-1=4a+2b+c
Replace all occurrences of c in -1=a+b+c with -5.
c=-5
-9=a-b-5
-1=a+b-5
-1=4a+2b+c
Replace all occurrences of c in -1=4a+2b+c with -5.
c=-5
-9=a-b-5
-1=a+b-5
-1=4a+2b-5
c=-5
-9=a-b-5
-1=a+b-5
-1=4a+2b-5
Simplify.
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Remove parentheses.
c=-5
-9=a-b-5
-1=a+b-5
-1=4a+2b-5
Remove parentheses.
c=-5
-9=a-b-5
-1=a+b-5
-1=4a+2b-5
Remove parentheses.
c=-5
-9=a-b-5
-1=a+b-5
-1=4a+2b-5
c=-5
-9=a-b-5
-1=a+b-5
-1=4a+2b-5
Solve for a in the second equation.
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Rewrite the equation as a-b-5=-9.
c=-5
a-b-5=-9
-1=a+b-5
-1=4a+2b-5
Move all terms not containing a to the right side of the equation.
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Add b to both sides of the equation.
c=-5
a-5=-9+b
-1=a+b-5
-1=4a+2b-5
Add 5 to both sides of the equation.
c=-5
a=-9+b+5
-1=a+b-5
-1=4a+2b-5
Add -9 and 5.
c=-5
a=b-4
-1=a+b-5
-1=4a+2b-5
c=-5
a=b-4
-1=a+b-5
-1=4a+2b-5
c=-5
a=b-4
-1=a+b-5
-1=4a+2b-5
Replace all occurrences of a with b-4 in each equation.
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Replace all occurrences of a in -1=a+b-5 with b-4.
c=-5
a=b-4
-1=(b-4)+b-5
-1=4a+2b-5
Replace all occurrences of a in -1=4a+2b-5 with b-4.
c=-5
a=b-4
-1=(b-4)+b-5
-1=4(b-4)+2b-5
c=-5
a=b-4
-1=(b-4)+b-5
-1=4(b-4)+2b-5
Simplify each equation.
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Simplify (b-4)+b-5.
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Add b and b.
c=-5
a=b-4
-1=2b-4-5
-1=4(b-4)+2b-5
Subtract 5 from -4.
c=-5
a=b-4
-1=2b-9
-1=4(b-4)+2b-5
c=-5
a=b-4
-1=2b-9
-1=4(b-4)+2b-5
Simplify 4(b-4)+2b-5.
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Simplify each term.
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Apply the distributive property.
c=-5
a=b-4
-1=2b-9
-1=4b+4⋅-4+2b-5
Multiply 4 by -4.
c=-5
a=b-4
-1=2b-9
-1=4b-16+2b-5
c=-5
a=b-4
-1=2b-9
-1=4b-16+2b-5
Simplify by adding terms.
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Add 4b and 2b.
c=-5
a=b-4
-1=2b-9
-1=6b-16-5
Subtract 5 from -16.
c=-5
a=b-4
-1=2b-9
-1=6b-21
c=-5
a=b-4
-1=2b-9
-1=6b-21
c=-5
a=b-4
-1=2b-9
-1=6b-21
c=-5
a=b-4
-1=2b-9
-1=6b-21
Solve for b in the third equation.
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Rewrite the equation as 2b-9=-1.
c=-5
a=b-4
2b-9=-1
-1=6b-21
Move all terms not containing b to the right side of the equation.
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Add 9 to both sides of the equation.
c=-5
a=b-4
2b=-1+9
-1=6b-21
Add -1 and 9.
c=-5
a=b-4
2b=8
-1=6b-21
c=-5
a=b-4
2b=8
-1=6b-21
Divide each term by 2 and simplify.
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Divide each term in 2b=8 by 2.
c=-5
a=b-4
2b2=82
-1=6b-21
Cancel the common factor of 2.
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Cancel the common factor.
c=-5
a=b-4
2b2=82
-1=6b-21
Divide b by 1.
c=-5
a=b-4
b=82
-1=6b-21
c=-5
a=b-4
b=82
-1=6b-21
Divide 8 by 2.
c=-5
a=b-4
b=4
-1=6b-21
c=-5
a=b-4
b=4
-1=6b-21
c=-5
a=b-4
b=4
-1=6b-21
Replace all occurrences of b with 4 in each equation.
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Replace all occurrences of b in a=b-4 with 4.
c=-5
a=(4)-4
b=4
-1=6b-21
Replace all occurrences of b in -1=6b-21 with 4.
c=-5
a=(4)-4
b=4
-1=6(4)-21
c=-5
a=(4)-4
b=4
-1=6(4)-21
Simplify.
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Subtract 4 from 4.
c=-5
a=0
b=4
-1=6(4)-21
Simplify 6(4)-21.
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Multiply 6 by 4.
c=-5
a=0
b=4
-1=24-21
Subtract 21 from 24.
c=-5
a=0
b=4
-1=3
c=-5
a=0
b=4
-1=3
c=-5
a=0
b=4
-1=3
Since -1≠3, there are no solutions.
c=-5
a=0
b=4
No solution
c=-5
a=0
b=4
No solution
Calculate the value of y using each x value in the table and compare this value to the given y value in the table.
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Calculate the value of y such that y=ax2+b when a=0, b=4, c=-5, and x=-1.
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Simplify each term.
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Raise -1 to the power of 2.
y=0⋅1+(4)⋅(-1)-5
Multiply 0 by 1.
y=0+(4)⋅(-1)-5
Multiply 4 by -1.
y=0-4-5
y=0-4-5
Simplify by subtracting numbers.
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Subtract 4 from 0.
y=-4-5
Subtract 5 from -4.
y=-9
y=-9
y=-9
If the table has a quadratic function rule, y=y for the corresponding x value, x=-1. This check passes since y=-9 and y=-9.
-9=-9
Calculate the value of y such that y=ax2+b when a=0, b=4, c=-5, and x=0.
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Simplify each term.
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Multiply 0 by (0)2 by adding the exponents.
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Multiply 0 by (0)2.
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Raise 0 to the power of 1.
y=0⋅(0)2+(4)⋅(0)-5
Use the power rule aman=am+n to combine exponents.
y=01+2+(4)⋅(0)-5
y=01+2+(4)⋅(0)-5
Add 1 and 2.
y=03+(4)⋅(0)-5
y=03+(4)⋅(0)-5
Raising 0 to any positive power yields 0.
y=0+(4)⋅(0)-5
Multiply 4 by 0.
y=0+0-5
y=0+0-5
Simplify by adding zeros.
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Add 0 and 0.
y=0-5
Subtract 5 from 0.
y=-5
y=-5
y=-5
If the table has a quadratic function rule, y=y for the corresponding x value, x=0. This check passes since y=-5 and y=-5.
-5=-5
Calculate the value of y such that y=ax2+b when a=0, b=4, c=-5, and x=1.
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Simplify each term.
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One to any power is one.
y=0⋅1+(4)⋅(1)-5
Multiply 0 by 1.
y=0+(4)⋅(1)-5
Multiply 4 by 1.
y=0+4-5
y=0+4-5
Simplify by subtracting numbers.
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Add 0 and 4.
y=4-5
Subtract 5 from 4.
y=-1
y=-1
y=-1
If the table has a quadratic function rule, y=y for the corresponding x value, x=1. This check passes since y=-1 and y=-1.
-1=-1
Calculate the value of y such that y=ax2+b when a=0, b=4, c=-5, and x=2.
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Simplify each term.
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Raise 2 to the power of 2.
y=0⋅4+(4)⋅(2)-5
Multiply 0 by 4.
y=0+(4)⋅(2)-5
Multiply 4 by 2.
y=0+8-5
y=0+8-5
Simplify by subtracting numbers.
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Add 0 and 8.
y=8-5
Subtract 5 from 8.
y=3
y=3
y=3
If the table has a quadratic function rule, y=y for the corresponding x value, x=2. This check does not pass, since y=3 and y=-1. The function rule can’t be quadratic.
3≠-1
Since y≠y for the corresponding x values, the function is not quadratic.
The function is not quadratic
The function is not quadratic
The function is not quadratic
Check if the function rule is cubic.
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To find if the table follows a function rule, check whether the function rule could follow the form y=ax3+bx2+cx+d.
y=ax3+bx2+cx+d
Build a set of 4 equations from the table such that y=ax3+bx2+cx+d.
Calculate the values of a, b, c, and d.
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Simplify each equation.
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Simplify each term.
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Raise -1 to the power of 3.
-9=a⋅-1+b(-1)2+c(-1)+d
-5=a(0)3+b(-1)2+c(-1)+d
-1=a(1)3+b(-1)2+c(-1)+d
-1=a(2)3+b(-1)2+c(-1)+d
Move -1 to the left of a.
-9=-1⋅a+b(-1)2+c(-1)+d
-5=a(0)3+b(-1)2+c(-1)+d
-1=a(1)3+b(-1)2+c(-1)+d
-1=a(2)3+b(-1)2+c(-1)+d
Rewrite -1a as -a.
-9=-a+b(-1)2+c(-1)+d
-5=a(0)3+b(-1)2+c(-1)+d
-1=a(1)3+b(-1)2+c(-1)+d
-1=a(2)3+b(-1)2+c(-1)+d
Raise -1 to the power of 2.
-9=-a+b⋅1+c(-1)+d
-5=a(0)3+b(-1)2+c(-1)+d
-1=a(1)3+b(-1)2+c(-1)+d
-1=a(2)3+b(-1)2+c(-1)+d
Multiply b by 1.
-9=-a+b+c(-1)+d
-5=a(0)3+b(-1)2+c(-1)+d
-1=a(1)3+b(-1)2+c(-1)+d
-1=a(2)3+b(-1)2+c(-1)+d
Move -1 to the left of c.
-9=-a+b-1⋅c+d
-5=a(0)3+b(-1)2+c(-1)+d
-1=a(1)3+b(-1)2+c(-1)+d
-1=a(2)3+b(-1)2+c(-1)+d
Rewrite -1c as -c.
-9=-a+b-c+d
-5=a(0)3+b(-1)2+c(-1)+d
-1=a(1)3+b(-1)2+c(-1)+d
-1=a(2)3+b(-1)2+c(-1)+d
-9=-a+b-c+d
-5=a(0)3+b(-1)2+c(-1)+d
-1=a(1)3+b(-1)2+c(-1)+d
-1=a(2)3+b(-1)2+c(-1)+d
Simplify a(0)3+b(-1)2+c(-1)+d.
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Simplify each term.
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Raising 0 to any positive power yields 0.
-9=-a+b-c+d
-5=a⋅0+b(-1)2+c(-1)+d
-1=a(1)3+b(-1)2+c(-1)+d
-1=a(2)3+b(-1)2+c(-1)+d
Multiply a by 0.
-9=-a+b-c+d
-5=0+b(-1)2+c(-1)+d
-1=a(1)3+b(-1)2+c(-1)+d
-1=a(2)3+b(-1)2+c(-1)+d
Raise -1 to the power of 2.
-9=-a+b-c+d
-5=0+b⋅1+c(-1)+d
-1=a(1)3+b(-1)2+c(-1)+d
-1=a(2)3+b(-1)2+c(-1)+d
Multiply b by 1.
-9=-a+b-c+d
-5=0+b+c(-1)+d
-1=a(1)3+b(-1)2+c(-1)+d
-1=a(2)3+b(-1)2+c(-1)+d
Move -1 to the left of c.
-9=-a+b-c+d
-5=0+b-1⋅c+d
-1=a(1)3+b(-1)2+c(-1)+d
-1=a(2)3+b(-1)2+c(-1)+d
Rewrite -1c as -c.
-9=-a+b-c+d
-5=0+b-c+d
-1=a(1)3+b(-1)2+c(-1)+d
-1=a(2)3+b(-1)2+c(-1)+d
-9=-a+b-c+d
-5=0+b-c+d
-1=a(1)3+b(-1)2+c(-1)+d
-1=a(2)3+b(-1)2+c(-1)+d
Add 0 and b.
-9=-a+b-c+d
-5=b-c+d
-1=a(1)3+b(-1)2+c(-1)+d
-1=a(2)3+b(-1)2+c(-1)+d
-9=-a+b-c+d
-5=b-c+d
-1=a(1)3+b(-1)2+c(-1)+d
-1=a(2)3+b(-1)2+c(-1)+d
Simplify each term.
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One to any power is one.
-9=-a+b-c+d
-5=b-c+d
-1=a⋅1+b(-1)2+c(-1)+d
-1=a(2)3+b(-1)2+c(-1)+d
Multiply a by 1.
-9=-a+b-c+d
-5=b-c+d
-1=a+b(-1)2+c(-1)+d
-1=a(2)3+b(-1)2+c(-1)+d
Raise -1 to the power of 2.
-9=-a+b-c+d
-5=b-c+d
-1=a+b⋅1+c(-1)+d
-1=a(2)3+b(-1)2+c(-1)+d
Multiply b by 1.
-9=-a+b-c+d
-5=b-c+d
-1=a+b+c(-1)+d
-1=a(2)3+b(-1)2+c(-1)+d
Move -1 to the left of c.
-9=-a+b-c+d
-5=b-c+d
-1=a+b-1⋅c+d
-1=a(2)3+b(-1)2+c(-1)+d
Rewrite -1c as -c.
-9=-a+b-c+d
-5=b-c+d
-1=a+b-c+d
-1=a(2)3+b(-1)2+c(-1)+d
-9=-a+b-c+d
-5=b-c+d
-1=a+b-c+d
-1=a(2)3+b(-1)2+c(-1)+d
Simplify each term.
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Raise 2 to the power of 3.
-9=-a+b-c+d
-5=b-c+d
-1=a+b-c+d
-1=a⋅8+b(-1)2+c(-1)+d
Move 8 to the left of a.
-9=-a+b-c+d
-5=b-c+d
-1=a+b-c+d
-1=8⋅a+b(-1)2+c(-1)+d
Raise -1 to the power of 2.
-9=-a+b-c+d
-5=b-c+d
-1=a+b-c+d
-1=8a+b⋅1+c(-1)+d
Multiply b by 1.
-9=-a+b-c+d
-5=b-c+d
-1=a+b-c+d
-1=8a+b+c(-1)+d
Move -1 to the left of c.
-9=-a+b-c+d
-5=b-c+d
-1=a+b-c+d
-1=8a+b-1⋅c+d
Rewrite -1c as -c.
-9=-a+b-c+d
-5=b-c+d
-1=a+b-c+d
-1=8a+b-c+d
-9=-a+b-c+d
-5=b-c+d
-1=a+b-c+d
-1=8a+b-c+d
-9=-a+b-c+d
-5=b-c+d
-1=a+b-c+d
-1=8a+b-c+d
Solve for b in the second equation.
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Rewrite the equation as b-c+d=-5.
-9=-a+b-c+d
b-c+d=-5
-1=a+b-c+d
-1=8a+b-c+d
Move all terms not containing b to the right side of the equation.
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Add c to both sides of the equation.
-9=-a+b-c+d
b+d=-5+c
-1=a+b-c+d
-1=8a+b-c+d
Subtract d from both sides of the equation.
-9=-a+b-c+d
b=-5+c-d
-1=a+b-c+d
-1=8a+b-c+d
-9=-a+b-c+d
b=-5+c-d
-1=a+b-c+d
-1=8a+b-c+d
-9=-a+b-c+d
b=-5+c-d
-1=a+b-c+d
-1=8a+b-c+d
Replace all occurrences of b with -5+c-d in each equation.
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Replace all occurrences of b in -9=-a+b-c+d with -5+c-d.
-9=-a-5+c-d-c+d
b=-5+c-d
-1=a+b-c+d
-1=8a+b-c+d
Replace all occurrences of b in -1=a+b-c+d with -5+c-d.
-9=-a-5+c-d-c+d
b=-5+c-d
-1=a-5+c-d-c+d
-1=8a+b-c+d
Replace all occurrences of b in -1=8a+b-c+d with -5+c-d.
-9=-a-5+c-d-c+d
b=-5+c-d
-1=a-5+c-d-c+d
-1=8a-5+c-d-c+d
-9=-a-5+c-d-c+d
b=-5+c-d
-1=a-5+c-d-c+d
-1=8a-5+c-d-c+d
Simplify each equation.
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Remove parentheses.
-9=-a-5+c-d-c+d
b=-5+c-d
-1=a-5+c-d-c+d
-1=8a-5+c-d-c+d
Combine the opposite terms in -a-5+c-d-c+d.
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Subtract c from c.
-9=-a-5-d+0+d
b=-5+c-d
-1=a-5+c-d-c+d
-1=8a-5+c-d-c+d
Add -a-5-d and 0.
-9=-a-5-d+d
b=-5+c-d
-1=a-5+c-d-c+d
-1=8a-5+c-d-c+d
Add -d and d.
-9=-a-5+0
b=-5+c-d
-1=a-5+c-d-c+d
-1=8a-5+c-d-c+d
Add -a-5 and 0.
-9=-a-5
b=-5+c-d
-1=a-5+c-d-c+d
-1=8a-5+c-d-c+d
-9=-a-5
b=-5+c-d
-1=a-5+c-d-c+d
-1=8a-5+c-d-c+d
Remove parentheses.
-9=-a-5
b=-5+c-d
-1=a-5+c-d-c+d
-1=8a-5+c-d-c+d
Combine the opposite terms in a-5+c-d-c+d.
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Subtract c from c.
-9=-a-5
b=-5+c-d
-1=a-5-d+0+d
-1=8a-5+c-d-c+d
Add a-5-d and 0.
-9=-a-5
b=-5+c-d
-1=a-5-d+d
-1=8a-5+c-d-c+d
Add -d and d.
-9=-a-5
b=-5+c-d
-1=a-5+0
-1=8a-5+c-d-c+d
Add a-5 and 0.
-9=-a-5
b=-5+c-d
-1=a-5
-1=8a-5+c-d-c+d
-9=-a-5
b=-5+c-d
-1=a-5
-1=8a-5+c-d-c+d
Remove parentheses.
-9=-a-5
b=-5+c-d
-1=a-5
-1=8a-5+c-d-c+d
Combine the opposite terms in 8a-5+c-d-c+d.
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Subtract c from c.
-9=-a-5
b=-5+c-d
-1=a-5
-1=8a-5-d+0+d
Add 8a-5-d and 0.
-9=-a-5
b=-5+c-d
-1=a-5
-1=8a-5-d+d
Add -d and d.
-9=-a-5
b=-5+c-d
-1=a-5
-1=8a-5+0
Add 8a-5 and 0.
-9=-a-5
b=-5+c-d
-1=a-5
-1=8a-5
-9=-a-5
b=-5+c-d
-1=a-5
-1=8a-5
-9=-a-5
b=-5+c-d
-1=a-5
-1=8a-5
Solve for a in the first equation.
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Rewrite the equation as -a-5=-9.
-a-5=-9
b=-5+c-d
-1=a-5
-1=8a-5
Move all terms not containing a to the right side of the equation.
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Add 5 to both sides of the equation.
-a=-9+5
b=-5+c-d
-1=a-5
-1=8a-5
Add -9 and 5.
-a=-4
b=-5+c-d
-1=a-5
-1=8a-5
-a=-4
b=-5+c-d
-1=a-5
-1=8a-5
Multiply each term in -a=-4 by -1
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Multiply each term in -a=-4 by -1.
(-a)⋅-1=(-4)⋅-1
b=-5+c-d
-1=a-5
-1=8a-5
Multiply (-a)⋅-1.
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Multiply -1 by -1.
1a=(-4)⋅-1
b=-5+c-d
-1=a-5
-1=8a-5
Multiply a by 1.
a=(-4)⋅-1
b=-5+c-d
-1=a-5
-1=8a-5
a=(-4)⋅-1
b=-5+c-d
-1=a-5
-1=8a-5
Multiply -4 by -1.
a=4
b=-5+c-d
-1=a-5
-1=8a-5
a=4
b=-5+c-d
-1=a-5
-1=8a-5
a=4
b=-5+c-d
-1=a-5
-1=8a-5
Replace all occurrences of a with 4 in each equation.
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Replace all occurrences of a in -1=a-5 with 4.
a=4
b=-5+c-d
-1=(4)-5
-1=8a-5
Replace all occurrences of a in -1=8a-5 with 4.
a=4
b=-5+c-d
-1=(4)-5
-1=8(4)-5
a=4
b=-5+c-d
-1=(4)-5
-1=8(4)-5
Simplify.
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Subtract 5 from 4.
a=4
b=-5+c-d
-1=-1
-1=8(4)-5
Simplify 8(4)-5.
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Multiply 8 by 4.
a=4
b=-5+c-d
-1=-1
-1=32-5
Subtract 5 from 32.
a=4
b=-5+c-d
-1=-1
-1=27
a=4
b=-5+c-d
-1=-1
-1=27
a=4
b=-5+c-d
-1=-1
-1=27
Since -1=-1, the equation will always be true.
a=4
b=-5+c-d
Always true
-1=27
Remove any equations from the system that are always true.
a=4
b=-5+c-d
-1=27
Since -1≠27, there are no solutions.
a=4
b=-5+c-d
Always true
No solution
Remove any equations from the system that are always true.
a=4
b=-5+c-d
No solution
a=4
b=-5+c-d
No solution
Calculate the value of y using each x value in the table and compare this value to the given y value in the table.
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Calculate the value of y such that y=ax3+b when a=4, b=-5+c-d, c=0, d=0, and x=-1.
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Simplify each term.
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Raise -1 to the power of 3.
y=4⋅-1+(-5+c-d)⋅(-12)+(0)⋅((-1)⋅0)
Multiply 4 by -1.
y=-4+(-5+c-d)⋅(-12)+(0)⋅((-1)⋅0)
One to any power is one.
y=-4+(-5+c-d)⋅(-1⋅1)+(0)⋅((-1)⋅0)
Multiply -1 by 1.
y=-4+(-5+c-d)⋅-1+(0)⋅((-1)⋅0)
Apply the distributive property.
y=-4-5⋅-1+c⋅-1-d⋅-1+(0)⋅((-1)⋅0)
Simplify.
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Multiply -5 by -1.
y=-4+5+c⋅-1-d⋅-1+(0)⋅((-1)⋅0)
Move -1 to the left of c.
y=-4+5-1⋅c-d⋅-1+(0)⋅((-1)⋅0)
Multiply -d⋅-1.
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Multiply -1 by -1.
y=-4+5-1⋅c+1d+(0)⋅((-1)⋅0)
Multiply d by 1.
y=-4+5-1⋅c+d+(0)⋅((-1)⋅0)
y=-4+5-1⋅c+d+(0)⋅((-1)⋅0)
y=-4+5-1⋅c+d+(0)⋅((-1)⋅0)
Rewrite -1c as -c.
y=-4+5-c+d+(0)⋅((-1)⋅0)
Multiply -1 by 0.
y=-4+5-c+d+0⋅0
Multiply 0 by 0.
y=-4+5-c+d+0
y=-4+5-c+d+0
Simplify by adding numbers.
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Add -4+5-c+d and 0.
y=-4+5-c+d
Add -4 and 5.
y=1-c+d
y=1-c+d
y=1-c+d
If the table has a cubic function rule, y=y for the corresponding x value, x=-1. This check does not pass, since y=1-c+d and y=-9. The function rule can’t be cubic.
1-c+d≠-9
Since y≠y for the corresponding x values, the function is not cubic.
The function is not cubic
The function is not cubic
The function is not cubic
There are no values for a, b, c, and d in the equations y=ax+b, y=ax2+bx+c, and y=ax3+bx2+cx+d that work for every pair of x and y.
The table does not have a function rule that is linear, quadratic, or cubic.
Find the Function Rule table[[x,y],[-1,-9],[0,-5],[1,-1],[2,-1]]

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