8x+5

Set the radicand in 2x greater than or equal to 0 to find where the expression is defined.

2x≥0

Divide each term by 2 and simplify.

Divide each term in 2x≥0 by 2.

2×2≥02

Cancel the common factor of 2.

Cancel the common factor.

2×2≥02

Divide x by 1.

x≥02

x≥02

Divide 0 by 2.

x≥0

x≥0

The domain is all values of x that make the expression defined.

Interval Notation:

[0,∞)

Set-Builder Notation:

{x|x≥0}

Interval Notation:

[0,∞)

Set-Builder Notation:

{x|x≥0}

Replace the variable x with 0 in the expression.

f(0)=22(0)+5

Simplify the result.

Simplify each term.

Multiply 2 by 0.

f(0)=20+5

Rewrite 0 as 02.

f(0)=202+5

Pull terms out from under the radical, assuming positive real numbers.

f(0)=2⋅0+5

Multiply 2 by 0.

f(0)=0+5

f(0)=0+5

Add 0 and 5.

f(0)=5

The final answer is 5.

5

5

5

The radical expression end point is (0,5).

(0,5)

Substitute the x value 1 into f(x)=22x+5. In this case, the point is (1,22+5).

Replace the variable x with 1 in the expression.

f(1)=22(1)+5

Simplify the result.

Multiply 2 by 1.

f(1)=22+5

The final answer is 22+5.

y=22+5

y=22+5

y=22+5

Substitute the x value 2 into f(x)=22x+5. In this case, the point is (2,9).

Replace the variable x with 2 in the expression.

f(2)=22(2)+5

Simplify the result.

Simplify each term.

Multiply 2 by 2.

f(2)=24+5

Rewrite 4 as 22.

f(2)=222+5

Pull terms out from under the radical, assuming positive real numbers.

f(2)=2⋅2+5

Multiply 2 by 2.

f(2)=4+5

f(2)=4+5

Add 4 and 5.

f(2)=9

The final answer is 9.

y=9

y=9

y=9

The square root can be graphed using the points around the vertex (0,5),(1,7.83),(2,9)

xy0517.8329

xy0517.8329

Graph square root of 8x+5