Inverses

To graph the inverse of a function...

• Rotate it around the origin

• Reflect it across the x-axis

• Reflect it across the y-axis

• Switch the x and y coordinates and plot the new points

Tags

CCSS.HSF.BF.B.4

CCSS.HSF.IF.C.7

Are these functions inverses of each other?

• Yes
• No

Tags

CCSS.HSF.BF.B.4

CCSS.HSF.IF.A.1

If the equation of f(x) goes through (1, 4) and (4, 6), what points does f^-1(x) go through?

• (1, 4) and (4, 6)
• (-4, -1) and (-6, -4)
• (-1, -4) and (-4, -6)
• (4, 1) and (6, 4)

Tags

CCSS.HSF.BF.B.4

Find the inverse of f(x) = x² - 5

• f^-1(x) = √(x) + 5
• f^-1(x) = ∛(x-5)
• f^-1(x) =√(x+5)
• f^-1(x) = x² - 5

Tags

CCSS.HSF-BF.B.4A

Is this function one to one?

• No, because the function does not pass the vertical and horizontal line test.

• Yes, because the function does not pass the vertical and horizontal line test.

• There is no way to tell.

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CCSS.HSF.IF.A.1

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Find the inverse of  $f\left(x\right)=\sqrt{x}+8$  

•  $f^{-1}\left(x\right)=x^2+8$  

•  $f^{-1}\left(x\right)=x^2-8$  

•  $f^{-1}\left(x\right)=\left(x+8\right)^2$  

•  $f^{-1}\left(x\right)=\left(x-8\right)^2$  

Tags

CCSS.HSF-BF.B.4A

Are these the graphs of two inverse functions?

• Yes
• No
• No way to tell

Tags

CCSS.HSF.BF.B.4

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.9

Are these inverse functions

• no
• yes
• no way to tell

Tags

CCSS.HSF.BF.B.4

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Suppose a function  $f\left(x\right)$  has domain  $\left[3,\infty\right)$  and range  $\left[0,\infty\right)$  .  What is the domain of  $f^{-1}\left(x\right)$ ?

•  $\left(-\infty,3\right]$  

•  $\left(-\infty,\ 0\right]$  

•  $\left[0,\ \infty\right)$  

•  $\left[3,\ \infty\right)$  

Tags

CCSS.HSF.BF.B.4

CCSS.HSF.IF.A.1

CCSS.HSF.IF.B.5

The domain of a function is All Real Numbers. What does that mean about the inverse of the function?

• The domain of the inverse is also All Real Numbers.

• The range of the inverse is All Real Numbers.

• The inverse must be a function.

• This doesn't tell me anything about the inverse.

Tags

CCSS.HSF.BF.B.4

CCSS.HSF.IF.A.1