g(x)=-5x+45

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.

Divide each term by 5 and simplify.

Divide each term in 5(-x+9)≥0 by 5.

5(-x+9)5≥05

Cancel the common factor of 5.

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

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.

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}

Replace the variable x with 9 in the expression.

f(9)=5(-(9)+9)

Simplify the result.

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)

Substitute the x value 7 into f(x)=5(-x+9). In this case, the point is (7,10).

Replace the variable x with 7 in the expression.

f(7)=5(-(7)+9)

Simplify the result.

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).

Replace the variable x with 8 in the expression.

f(8)=5(-(8)+9)

Simplify the result.

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