g(x)=-3x+4

Set the radicand in 3x+4 greater than or equal to 0 to find where the expression is defined.

3x+4≥0

Solve for x.

Subtract 4 from both sides of the inequality.

3x≥-4

Divide each term by 3 and simplify.

Divide each term in 3x≥-4 by 3.

3×3≥-43

Cancel the common factor of 3.

Cancel the common factor.

3×3≥-43

Divide x by 1.

x≥-43

x≥-43

Move the negative in front of the fraction.

x≥-43

x≥-43

x≥-43

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

Interval Notation:

[-43,∞)

Set-Builder Notation:

{x|x≥-43}

Interval Notation:

[-43,∞)

Set-Builder Notation:

{x|x≥-43}

Replace the variable x with -43 in the expression.

f(-43)=-3(-43)+4

Simplify the result.

Cancel the common factor of 3.

Move the leading negative in -43 into the numerator.

f(-43)=-3(-43)+4

Cancel the common factor.

f(-43)=-3(-43)+4

Rewrite the expression.

f(-43)=–4+4

f(-43)=–4+4

Simplify the expression.

Add -4 and 4.

f(-43)=-0

Rewrite 0 as 02.

f(-43)=-02

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

f(-43)=-0

Multiply -1 by 0.

f(-43)=0

f(-43)=0

The final answer is 0.

0

0

0

The radical expression end point is (-43,0).

(-43,0)

Substitute the x value -1 into f(x)=-3x+4. In this case, the point is (-1,-1).

Replace the variable x with -1 in the expression.

f(-1)=-3(-1)+4

Simplify the result.

Multiply 3 by -1.

f(-1)=–3+4

Add -3 and 4.

f(-1)=-1

Any root of 1 is 1.

f(-1)=-1⋅1

Multiply -1 by 1.

f(-1)=-1

The final answer is -1.

y=-1

y=-1

y=-1

Substitute the x value 0 into f(x)=-3x+4. In this case, the point is (0,-2).

Replace the variable x with 0 in the expression.

f(0)=-3(0)+4

Simplify the result.

Multiply 3 by 0.

f(0)=-0+4

Add 0 and 4.

f(0)=-4

Rewrite 4 as 22.

f(0)=-22

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

f(0)=-1⋅2

Multiply -1 by 2.

f(0)=-2

The final answer is -2.

y=-2

y=-2

y=-2

Substitute the x value 1 into f(x)=-3x+4. In this case, the point is (1,-7).

Replace the variable x with 1 in the expression.

f(1)=-3(1)+4

Simplify the result.

Multiply 3 by 1.

f(1)=-3+4

Add 3 and 4.

f(1)=-7

The final answer is -7.

y=-7

y=-7

y=-7

The square root can be graphed using the points around the vertex (-1.3‾,0),(-1,-1),(0,-2),(1,-2.65)

xy-1.3330-1-10-21-2.65

xy-1.3330-1-10-21-2.65

Graph g(x)=- square root of 3x+4