NC.M3.U1.F-BF.4a&b Re-Test Lesson

​NC Math 3 Unit 1 Re-Test Lesson
Standard(s): F-BF.4a&b

​​Instructions:
Earn an 80% or higher on this lesson to be able to re-attempt the questions that you missed tied to this standard from our Unit 1 test.

Inverse Graphs

• Symmetrical across the line y=x

• Points on f(x) like (2, 4)

• becomes on f^-1(x) as (4, 2)

Multiple Choice

Are these functions inverses?

• Yes
• No

Multiple Choice

Are the blue and red graphs inverse functions?

• yes
• no
• no way to tell

Multiple Choice

Are these inverse functions?

• no
• yes
• no way to tell

Multiple Choice

The inverse has been reflected over which line?

• y = x
• y =1
• y = 0
• y = x + 1

Multiple Choice

What does it mean to find the inverse of a function?

• the x's and y's are switched
• the x's and y's are divided by 2
• the x's and y's are made negative
• the x's and y's are the same

Generating the inverse of Quadratics

​

When we remove half of the parabola, we successfully restrict the domain of f(x) in order for f and g to be inverses.

​

​f(x)

​g(x)

The functions f(x) and g(x) are graphed together on the same plane above. Since f and g are inverses, they should be symmetric across the line y=x.
Because this is not a mirror image across y=x like it should be, we must restrict the domain of the parabola.

If we remove the left side of the parabola, we will have the same graph on each side of the line y=x.

​f(x)

​g(x)

​f(x)

​g(x)

Multiple Choice

What is the domain of g(x)?

• $$\left(-\infty,0\right)$$

• $$\left[0,\ \infty\right)$$

• all real numbers

• $$\left[2,\ \infty\right)$$

Multiple Choice

What is the restricted domain of f(x)?

• $$\left(-\infty,0\right)$$

• $$\left[0,\ \infty\right)$$

• all real numbers

• $$\left[2,\ \infty\right)$$

Multiple Choice

Is the graph a function? Hint: use the vertical line test.

• yes

• no

Multiple Choice

What is a possible domain restriction for the inverse of the following function?

P (x) = 2x² + 1

• $$\left[0,\infty\right)$$

• $$\left(-\infty,1\right]$$

• $$\left[2,\infty\right)$$

• $$\left(-\infty,2\right]$$

Multiple Choice

What is a possible domain restriction for the inverse of the following function?

$$f\left(x\right)=\frac{1}{4}\left(x+1\right)^2$$  

•   $$\left[-1,\infty\right)$$

•   $$\left(-\infty,\frac{1}{4}\right]$$

• $$\left[0,\infty\right)$$  

Multiple Choice

What is a possible domain restriction for the inverse of the following function?

$$f\left(x\right)=4\left(x+3\right)^2$$  

•   $$\left[-3,\infty\right)$$

•   $$\left[0,\infty\right)$$

•   $$\left(-\infty,4\right]$$