6.01 to 6.03 Review 2024

6.01 to 6.03

Multiple Select

What are the solutions/zeros of the graph? Select all the correct answers.

• 3

• -3

• 2

• -2

• 5

Zeros and Multiplicity

Type of equation/degree

Write the function using zeros!

Multiple Choice

Name the function.

• Cubic

• Quadratic

• Rational

• Linear

• Exponential

Multiple Select

What are the roots?

• 0

• -2

• 1

• -1

• 3

Zeros and Multiplicity

Type of equation/degree

Write the function using zeros!

Fill in the Blanks

How many real solutions does the graph have?

Type in

0 1 or 2

It touches the x axis twice,
2 real solutions,
2 imaginary

4th degree polynomial 4 solutions

What is the polynomial if the zeros are 0, 2, -5 ?

Plug the zeros in as factors (use opposite sign)

Multiple Choice

What is the polynomial is the zeros are 0, -3, and 7?

• $$x^3+4x^2-21x$$

• $$x^3-4x^2-21x$$

• $$x^3+4x^2+21x$$

• $$x^3-4x^2+21x$$

Multiple Select

What are the roots of the function $$f\left(x\right)=4\left(x-2\right)^2\left(x+9\right)\left(x-7\right)$$

• -2

• 2

• -9

• -7

• 7

Fill in the Blanks

Imaginary Solutions always come in pairs.

Type

true or false

Fill in the Blanks

What is the pair for the imaginary number $6i$ ?

Type your answer in the blank. Do not use the space bar.

Multiple Choice

What is the pair for the imaginary number $$-3+7i?$$

• $$3-7i$$

• $$-3-7i$$

• $$-3+7i$$

• $$3+7i$$

​-1, 4 – 2i, 6i 

5, -7, 3 + 7i

Determine the least degree given the zeros
(count each imaginary solution twice)

Fill in the Blanks

What is the least degree for a function with solutions of 2, 3i?

only type the number

Fill in the Blanks

What is the least degree for a function with solutions of -5 , 2-i, -5i?

only type the number

​Find f(g(x))

​Find g(f(x))

Multiple Choice

Given f(x) = 2x - 3 and g(x) = $$-5x^2+4$$

find g(f(x))

• $$-20x^2+60x-43$$

• $$-10x^2+30x+2$$

• $$-20x^2-60x-43$$

• $$100x^2-300x+227$$

​Find g(f(-2))

Fill in the Blanks

Type your final answer in the blank. Do not use space bar. Just type the value.

Open Ended

What does the word "inverse" mean to you? Write your response in the blank given.

Multiple Choice

Write the equation in terms of y: $$4y-2x+8=16$$

• $$y\ =\ 2x\ +\ 2$$

• $$y=\frac{1}{2}x+2$$

• $$y=-2x+2$$

• $$y=-\frac{1}{2}x-2$$

​Find the inverse of a given function

​Find the inverse of a given function

Draw

Write the inverse of the given function

$$y=\frac{x-3}{6}$$

Draw

Write the inverse of the equation

$$f\left(x\right)=\sqrt[]{x-6}$$ ?

Multiple Choice

What is the inverse of the function $$y=x^2-7$$ ?

• $$y^{-1}=y+7$$

• $$y^{-1}=\sqrt[]{x+7}$$

• $$y^{-1}=\sqrt[]{x-7}$$

• $$y^{-1}=\sqrt[]{x^2+7}$$

Multiple Select

Which equation/equations(s) represent the inverse of the function $$f\left(x\right)=5x-2$$ ?

• $$f^{-1}\left(x\right)=\frac{2x}{5}$$

• $$y^{-1}=\frac{x}{5}+\frac{2}{5}$$

• $$f^{-1}\left(x\right)=\frac{x+5}{2}$$

• $$f^{-1}\left(x\right)=\frac{x+2}{5}$$

Multiple Choice

What is the inverse of the function? $$f\left(x\right)=\left(x-1\right)^3+4$$ ?

• $$f^{-1}\left(x\right)=\left(x-4\right)^3+1$$

• $$f^{-1}\left(x\right)=\sqrt[3]{x-4}+1$$

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

• $$f^{-1}\left(x\right)=\left(x\right)^3-3$$

Draw

Plot the points listed below on the graph given.

(2,0)

(3,4)

(-1,3)

(-4,-1)

(5,-4)

​The inverse graph will reflect off the y = x line! take points from the original graph, and switch x and y values. Plot those points.

Draw

Graph the inverse $$f^{-1}\left(x\right)$$ of the function given.