Unit 5 Review

Unit 5 Review

By Alexis Galt

Radical

​Be comfortable going back and forth from rational exponents to radical form.

Exponential and Radical Form

Some text here about the topic of discussion

Multiple Select

Which are equal to $$64^{\frac{2}{3}}$$   (Choose all correct answers)

• 8

• 16

• $$\left(\sqrt[3]{64}\right)^2$$  

• $$\left(\sqrt[2]{64}\right)^3$$  

Multiple Choice

Simplify: Give answer in exponential form.

$$\left(1000x^2y^5\right)^{\frac{1}{3}}$$  

• $$10x^{\frac{2}{3}}y^{\frac{5}{3}}$$  

• $$1000x^{\frac{2}{3}}y^{\frac{5}{3}}$$  

• $$333.333x^{.667}y^{1.667}$$  

• $$10x^{\frac{3}{2}}y^{\frac{3}{5}}$$  

Multiple Choice

Simplify: Give answer in reduced radical form.

$$\left(1000x^2y^5\right)^{\frac{1}{3}}$$  

• $$10\sqrt[3]{x^2y^5}$$  

• $$\sqrt[3]{10x^2y^5}$$  

• $$10x^2y^5\sqrt[3]{xy}$$  

• $$10y\sqrt[3]{x^2y^2}$$  

Be able to reduce radicals

Some text here about the topic of discussion

Multiple Choice

$$\sqrt[3]{54x^5y^7}$$  Simplify

• $$18xy\sqrt[3]{xy^2}$$  

• $$3x^3y^6\sqrt[3]{2x^2y}$$  

• $$2x^2y\sqrt[3]{3xy^2}$$  

• $$3xy^2\sqrt[3]{2x^2y}$$  

Be able to graph square and cube roots

Understand Stretches and compressions

Be able to plot translations right and left and up and down.

Some text here about the topic of discussion

Multiple Choice

What are the transformations of parent function for this function?

$$f\left(x\right)=2\sqrt[]{x-3}+1$$  

• Translation right 2 and down 3. No stretch or compression.

• Vertical stretch by a factor of 2.

  Translation 3 left.

  Translation 1 up.

• Vertical stretch by a factor of 2.

  Translation 3 right.

  Translation 1 up.

• Vertical compression of 1/2.

  Translation left 1.

  Translation down 3.

Draw

Sketch a graph of   $$f\left(x\right)=\sqrt[3]{x+2}+1$$  

Multiple Choice

Find the equation for this graph, given that there is no vertical stretch or compression of the parent function.

• $$f\left(x\right)=\sqrt[]{x}$$  

• $$f\left(x\right)=\sqrt[]{x+1}-3$$  

• $$g\left(x\right)=\sqrt[3]{x+1}-3$$  

• $$f\left(x\right)=\sqrt[]{x-1}-3$$  

Multiple Select

What are the domain and range for this graph. Choose a range and a domain.

• Domain: All real numbers 

• Domain $$\left[-1,\infty\right)$$   

• Range: All real numbers 

• Range $$\left[-3,\infty\right)$$   

• Domain and Range both: $$\left[0,\ \infty\right)$$  

Be Able to Solve a Radical Equation

​Steps

1. Isolate the radical expression group

2. Square or cube to free the radical

3. Solve for x​

4. Check for extraneous solutions​

Some text here about the topic of discussion

Multiple Choice

Solve

$$3\sqrt[]{x-3}+12=30$$  

• No Solution

• x = 9

• x = 39 and x = -33

• x= 39

​Be able to perform operations on functions

• Addition

• Subtraction

• Multiplication

• Division

• Composition of functions​

Subject | Subject

Some text here about the topic of discussion

Multiple Choice

$$f\left(x\right)=2x^2+3x$$   $$g\left(x\right)=3x-1$$  

Find g - f

(Note: These will be the same equations for the next four slides)

• $$2x^2+6x-1$$  

• $$-2x^2-1$$  

• $$2x^2+1$$  

• $$2x^2-1$$  

Multiple Choice

$$f\left(x\right)=2x^2+3x$$   $$g\left(x\right)=3x-1$$  

Find $$g\cdot f$$  

(Note: These will be the same equations for the next three slides)

• $$7x^4+6x^3-3x$$  

• $$6x^3-11x^2-3x$$  

• $$6x^3+7x^2-3x$$  

• $$5x^2+4x-3$$  

Multiple Choice

$$f\left(x\right)=2x^2+3x$$   $$g\left(x\right)=3x-1$$  

Find g(f(-2))

(Note: These will be the same equations for the next two slides)

• 5

•  2

•  -43

•  77

Multiple Choice

$$f\left(x\right)=2x^2+3x$$   $$g\left(x\right)=3x-1$$  

Find f(g(-2))

(Note: These will be the same equations for the next slide)

• 5

•  2

•  -43

•  77

Multiple Choice

$$f\left(x\right)=2x^2+3x$$   $$g\left(x\right)=3x-1$$  

Find f(g(x))

• $$\left(2x^2+3x\right)\left(3x-1\right)$$  

•   $$2\left(3x-1\right)^2+3\left(3x-1\right)$$  

• $$2x^2\left(3x-1\right)+3x\left(3x-1\right)$$   

Know how to work with inverses

Table: Switch the x and y coordinates

Graph: The inverse is a reflection across y = x

Equation: Switch x and y in the equation and then solve for y​

Subject | Subject

Some text here about the topic of discussion

Multiple Choice

$$y=x^2-3$$   for $$x\ge0$$  

What is the inverse equation?

•   $$y=\sqrt[]{x}+3$$  

• $$y+3=x^2$$  

• $$y=\sqrt[]{x+3}$$  

• $$\sqrt[]{y}=x+3$$