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

xy-1-90-51-12-1
Check if the function rule is linear.
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.
Simplify each equation.
Simplify a(0)+b.
Multiply a by 0.
-5=0+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
-5=b
-9=a(-1)+b
-1=a(1)+b
-1=a(2)+b
Simplify each term.
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.
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.
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.
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.
Add 5 to both sides of the equation.
b=-5
-a=-9+5
-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
Multiply each term in -a=-4 by -1
Multiply each term in -a=-4 by -1.
b=-5
(-a)⋅-1=(-4)⋅-1
-1=a-5
-1=2a-5
Multiply (-a)⋅-1.
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.
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.
Subtract 5 from 4.
b=-5
a=4
-1=-1
-1=2(4)-5
Simplify 2(4)-5.
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.
Calculate the value of y when a=4, b=-5, and x=-1.
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.
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.
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.
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.
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.
Simplify each equation.
Simplify a(0)2+b(0)+c.
Simplify each term.
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.
-5=0+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
-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.
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.
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.
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.
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.
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.
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.
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
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.
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.
Simplify (b-4)+b-5.
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.
Simplify each term.
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
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.
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.
Add 9 to both sides of the equation.
c=-5
a=b-4
2b=-1+9
-1=6b-21
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.
Divide each term in 2b=8 by 2.
c=-5
a=b-4
2b2=82
-1=6b-21
Cancel the common factor of 2.
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.
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.
Subtract 4 from 4.
c=-5
a=0
b=4
-1=6(4)-21
Simplify 6(4)-21.
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.
Calculate the value of y such that y=ax2+b when a=0, b=4, c=-5, and x=-1.
Simplify each term.
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.
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.
Simplify each term.
Multiply 0 by (0)2 by adding the exponents.
Multiply 0 by (0)2.
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
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
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.
Simplify each term.
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.
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.
Simplify each term.
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.
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.
Check if the function rule is cubic.
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.
Simplify each equation.
Simplify each term.
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.
Simplify each term.
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
-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.
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.
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.
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.
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.
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.
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.
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
-9=-a-5-d+d
b=-5+c-d
-1=a-5+c-d-c+d
-1=8a-5+c-d-c+d
-9=-a-5+0
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
-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.
Subtract c from c.
-9=-a-5
b=-5+c-d
-1=a-5-d+0+d
-1=8a-5+c-d-c+d
-9=-a-5
b=-5+c-d
-1=a-5-d+d
-1=8a-5+c-d-c+d
-9=-a-5
b=-5+c-d
-1=a-5+0
-1=8a-5+c-d-c+d
-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.
Subtract c from c.
-9=-a-5
b=-5+c-d
-1=a-5
-1=8a-5-d+0+d
-9=-a-5
b=-5+c-d
-1=a-5
-1=8a-5-d+d
-9=-a-5
b=-5+c-d
-1=a-5
-1=8a-5+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.
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.
Add 5 to both sides of the equation.
-a=-9+5
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
Multiply each term in -a=-4 by -1
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.
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.
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.
Subtract 5 from 4.
a=4
b=-5+c-d
-1=-1
-1=8(4)-5
Simplify 8(4)-5.
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.
Calculate the value of y such that y=ax3+b when a=4, b=-5+c-d, c=0, d=0, and x=-1.
Simplify each term.
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.
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.
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
y=-4+5-c+d
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]]