Unit 6 Test A: Radical Functions

3

Find the perimeter of the triangle below. Write your answer in simplest radical form.

3

Simplify the expression below.
\sqrt{18}{(2+\sqrt6})-2\sqrt{3}

3

Simplify the expression:
\frac{\sqrt{294k^{30}}}{\sqrt{3k^5}}

3

Which is equivalent to the expression below:
a^\frac{5}{4}b^\frac{13}{4}

2

Simplify the expression. Write the answer as a radical
\frac{8^\frac{7}{3}}{8^\frac{5}{3}}

4

Solve the equation:
7-(3k-29)^\frac{1}{4}=5

3

Solve the equation:
(7-3c)^{\frac{1}{2}}=(1-5c)^\frac{1}{2}

4

OPTIONAL: Solve for y:
\sqrt{6y+15}-4=y

2

The square root parent function is translated so that the endpoint is located at (-4,1). Write an equation that represents this new function.

4

What transformations take place by graphig the function below with respect to it's parent functions? Check all that apply.

f(x)=-3\sqrt{x-5}-4

7

Graph the function AND identify it's key characterisics.
f(x)=-\frac{1}{2}\sqrt{x}-3

Domain: {x|x _______ }  - use >= for 'greater than and equal to'
Range: {y|y_______ }
End Behaviour: As  x\rightarrow_______ , f(x)\rightarrow_______ use the word 'infinity'
                              As  x\rightarrow_______,  f(x)\rightarrow_______ 
Increasing Interval: _______ 
Decreasing Interval: _______ 
Endpoint: _______ 

2

Which of the following relations represent a one-to-one function? Check all that apply:

2

Find the inverse function.

3

Find the inverse functon.

ANSWER:
f^{-1}x=

3

Determine if the functions below are inverse functions. Prove your answer algebraically.
f(x)=\frac{1}{3}x-3 and g(x)=6x+18

4

OPTIONAL: Determine if the functions below are inverse functions. Prove your answer algebraically.
f(x)=\sqrt{x}+3 and g(x)=x^{2}-6x+9 if (x\geq{3})

4

Find the perimeter of the triangle below. Write your answer in simplest radical form.

Simplify the expression below.\sqrt{18}{(2+\sqrt6})-2\sqrt{3}

Simplify the expression:\frac{\sqrt{294k^{30}}}{\sqrt{3k^5}}

Which is equivalent to the expression below:a^\frac{5}{4}b^\frac{13}{4}

Simplify the expression. Write the answer as a radical\frac{8^\frac{7}{3}}{8^\frac{5}{3}}

Solve the equation:7-(3k-29)^\frac{1}{4}=5

Solve the equation:(7-3c)^{\frac{1}{2}}=(1-5c)^\frac{1}{2}

OPTIONAL: Solve for y:\sqrt{6y+15}-4=y

The square root parent function is translated so that the endpoint is located at (-4,1). Write an equation that represents this new function.

What transformations take place by graphig the function below with respect to it's parent functions? Check all that apply.f(x)=-3\sqrt{x-5}-4

Which of the following relations represent a one-to-one function? Check all that apply:

Find the inverse function.

Find the inverse functon. ANSWER:f^{-1}x=

Determine if the functions below are inverse functions. Prove your answer algebraically. f(x)=\frac{1}{3}x-3 and g(x)=6x+18

OPTIONAL: Determine if the functions below are inverse functions. Prove your answer algebraically.f(x)=\sqrt{x}+3 and g(x)=x^{2}-6x+9 if (x\geq{3})

OPTIONAL: Solve the equation\sqrt[3]{8x^{3}-1}+1=2x

Simplify the expression below.
\sqrt{18}{(2+\sqrt6})-2\sqrt{3}

Simplify the expression:
\frac{\sqrt{294k^{30}}}{\sqrt{3k^5}}

Which is equivalent to the expression below:
a^\frac{5}{4}b^\frac{13}{4}

Simplify the expression. Write the answer as a radical
\frac{8^\frac{7}{3}}{8^\frac{5}{3}}

Solve the equation:
7-(3k-29)^\frac{1}{4}=5

Solve the equation:
(7-3c)^{\frac{1}{2}}=(1-5c)^\frac{1}{2}

OPTIONAL: Solve for y:
\sqrt{6y+15}-4=y

What transformations take place by graphig the function below with respect to it's parent functions? Check all that apply.

f(x)=-3\sqrt{x-5}-4

Find the inverse functon.

ANSWER:
f^{-1}x=

Determine if the functions below are inverse functions. Prove your answer algebraically.
f(x)=\frac{1}{3}x-3 and g(x)=6x+18

OPTIONAL: Determine if the functions below are inverse functions. Prove your answer algebraically.
f(x)=\sqrt{x}+3 and g(x)=x^{2}-6x+9 if (x\geq{3})

OPTIONAL: Solve the equation
\sqrt[3]{8x^{3}-1}+1=2x