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 Blank

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 Blank

Imaginary Solutions always come in pairs.

Type

true or false

Fill in the Blank

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 Blank

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

only type the number

Fill in the Blank

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 Blank

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.