Chapter 6 Review Part 1

Chapter 6 Review Part 1

Rational and Radical Functions

Rewriting

• Remember "power/root"

Multiple Choice

1) Rewrite in exponential form:

• $x^{\frac{4}{7}}$

• $x^{\frac{7}{4}}$

• $\frac{1}{x^{\frac{4}{7}}}$

• $\frac{1}{x^{\frac{7}{4}}}$

Multiple Choice

2) Rewrite in exponential form:

• $\left(7x\right)^{\frac{3}{2}}$

• $\left(7x\right)^{\frac{1}{3}}$

• $\left(7x\right)^{\frac{1}{2}}$

• $\left(7x\right)^{\frac{2}{3}}$

Multiple Choice

 $3)\ Write\ in\ radical\ form:\ \left(2p\right)^{\frac{5}{6}}$  

Properties of Rational Exponents

Multiple Choice

4) What is the first step to simplifying this problem?

• Add the exponents on the inside of the parentheses.

• Add the exponents for the same bases on the outside of the parentheses.

• Multiply the exponent 3/2 to the exponents on the inside of the parentheses.

Multiple Choice

5) Simplify:

Multiple Choice

6) What do you do after you distribute the exponents in the denominator? What is the second step??

• You add the exponents for the variables with the same base.

• You multiply the exponents for the variables with the same base.

• You subtract the exponents for the variables with the same base.

• You cancel out the common factors.

Multiple Choice

7) When you fully simplify this problem, what is the exponent for base "a?"

• $\frac{11}{6}$

• $-\frac{13}{6}$

• $\frac{13}{6}$

• $-\frac{11}{6}$

Simplifying Radical Expressions

You can multiply two radicals with the same index.

You can divide two radicals with the same index.

You can add/subtract like radicals.

Multiple Choice

8) Simplify:   $\frac{5\sqrt{2}}{3\sqrt{18}}$  

**Hint** Divide the like radicals/reduce the fraction.

•  $\frac{5}{9}$  

•  $\frac{1}{5}$  

•  $\frac{9}{5}$  

•  $2$  

Multiple Choice

9) Simplify:  $\sqrt{3x}\cdot5\sqrt{15x}$  

•  $45$  

•  $15x\sqrt{5}$  

•  $3\sqrt{5}$  

•  $3x\sqrt{5}$  

Multiple Choice

 10) Simplify: $-2\sqrt{6}-\sqrt{6}$ 

•  $-2\sqrt{6}$  

•  $2\sqrt{6}$  

•  $-3\sqrt{6}$  

•  $-5\sqrt{6}$  

Combinations of Functions

• Add/Subtract like terms

• Multiply using distribution, FOIL, BOX methods

• Evaluate

• Plug one function into another

Multiple Choice

11)

• A

• B

• C

• D

Multiple Choice

12)   $f\left(x\right)=2x+1;\ Find\ f\left(2\right)$  

• -13

• 17

• -1

• 5

Multiple Choice

13) Perform the indicated operation (adding functions).

• $x^2-7x-1$

• $x^2+2x+2$

• $x^2-7x+1$

• $-2x^2-3x+4$

Multiple Choice

14) Perform the indicated operation.

• A

• B

• C

• D

Finding inverse functions

• Switch x and y (the input and the output)

• Solve for y

• That is the inverse!

Multiple Choice

15) Find the inverse of the function shown.

• A

• B

• C

• D

Multiple Choice

16) The inverse of  $y=2x^3$  is.....

•  $y^{-1}=\frac{x^3}{2}$  

•  $y^{-1}=\ ^3\sqrt{\frac{x}{2}}$  

•  $y^{-1}=\frac{^3\sqrt{x}}{2}$  

•  $y^{-1}=2x^3$  

Multiple Select

17) How do you know these linear functions are inverses of each other? (Select all correct answers)

• Their x's and y's are switched.

• They are symmetric about the line y = x.

• The slopes are reciprocals.

• They like each other.

Graphing Square and Cube Root Functions

Multiple Select

18) What are the difference(s) between the function shown and the parent graph of all square roots? 

 $y=-3\sqrt{x}$ 

  $Parent\ Graph:\ y\ =\ \sqrt{x}$  
(Select all that apply, use Desmos to graph if needed)

• Vertical shrink

• Vertical stretch

• Shifted down 3 units

• Flipped upside down (x-axis reflection)

Multiple Select

19) What number shifts the graph up and down?

 $y=a\sqrt{x-h}+k$  

• a

• h

• k

• x

• y