Graph g(x) = square root of -5x+45

Math
g(x)=-5x+45
Find the domain for y=-5x+45 so that a list of x values can be picked to find a list of points, which will help graphing the radical.
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Set the radicand in 5(-x+9) greater than or equal to 0 to find where the expression is defined.
5(-x+9)≥0
Solve for x.
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Divide each term by 5 and simplify.
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Divide each term in 5(-x+9)≥0 by 5.
5(-x+9)5≥05
Cancel the common factor of 5.
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Cancel the common factor.
5(-x+9)5≥05
Divide -x+9 by 1.
-x+9≥05
-x+9≥05
Divide 0 by 5.
-x+9≥0
-x+9≥0
Subtract 9 from both sides of the inequality.
-x≥-9
Multiply each term in -x≥-9 by -1
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Multiply each term in -x≥-9 by -1. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
(-x)⋅-1≤(-9)⋅-1
Multiply (-x)⋅-1.
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Multiply -1 by -1.
1x≤(-9)⋅-1
Multiply x by 1.
x≤(-9)⋅-1
x≤(-9)⋅-1
Multiply -9 by -1.
x≤9
x≤9
x≤9
The domain is all values of x that make the expression defined.
Interval Notation:
(-∞,9]
Set-Builder Notation:
{x|x≤9}
Interval Notation:
(-∞,9]
Set-Builder Notation:
{x|x≤9}
To find the radical expression end point, substitute the x value 9, which is the least value in the domain, into f(x)=5(-x+9).
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Replace the variable x with 9 in the expression.
f(9)=5(-(9)+9)
Simplify the result.
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Multiply -1 by 9.
f(9)=5(-9+9)
Add -9 and 9.
f(9)=5⋅0
Multiply 5 by 0.
f(9)=0
Rewrite 0 as 02.
f(9)=02
Pull terms out from under the radical, assuming positive real numbers.
f(9)=0
The final answer is 0.
0
0
0
The radical expression end point is (9,0).
(9,0)
Select a few x values from the domain. It would be more useful to select the values so that they are next to the x value of the radical expression end point.
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Substitute the x value 7 into f(x)=5(-x+9). In this case, the point is (7,10).
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Replace the variable x with 7 in the expression.
f(7)=5(-(7)+9)
Simplify the result.
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Multiply -1 by 7.
f(7)=5(-7+9)
Add -7 and 9.
f(7)=5⋅2
Multiply 5 by 2.
f(7)=10
The final answer is 10.
y=10
y=10
y=10
Substitute the x value 8 into f(x)=5(-x+9). In this case, the point is (8,5).
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Replace the variable x with 8 in the expression.
f(8)=5(-(8)+9)
Simplify the result.
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Multiply -1 by 8.
f(8)=5(-8+9)
Add -8 and 9.
f(8)=5⋅1
Multiply 5 by 1.
f(8)=5
The final answer is 5.
y=5
y=5
y=5
The square root can be graphed using the points around the vertex (9,0),(7,3.16),(8,2.24)
xy73.1682.2490
xy73.1682.2490
Graph g(x) = square root of -5x+45

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