Inverses and Translations

Do Now

Label each transformation


1. 2f(x)+5 =

2. f(-x)+2 =

3. f(x+3) =

Function
Inverses
Mr. Brown 204B

What is a function Inverse?

A "function inverse" is a mathematical function that essentially "undoes" the operations of another function, meaning if you apply one function and then its inverse to a value, you get back the original value; the inverse of a function f is often denoted as f^(-1)

-If f(x) = y, then the inverse function, f^(-1)(y) = x

-To find the inverse: Switch the x and y variables in
the function equation and solve for y.

Multiple Choice

What is the notation of an inverse?

• A^2
• f(x)
• A'
• A^{-1} or f^{-1}(x)

Fill in the Blank

What is needed to switch around when finding inverse?

&

Drag and Drop

Labels steps to find inverse?​ ​

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Drag these tiles and drop them in the correct blank above

Swop out variable

Switch F(x) to y=

Solve for y

replace y= with f^-1

solve for x

switch out y to f(x)

replacef^-1 with y=

Keep variables the same

List of Operations and Inverses.

Identify Correct Inverses.

Multiple Choice

What is the inverse of Squaring?

• Cubing
• Square root
• Halving
• Doubling

​We Do/ Think Pair Share - Find The Inverse


g(x) = −4x + 1

​We Do / Think Pair Share - Find Inverse

f (x) = −1 − 1/5 x

​We Do/ Think Pair Share - Find Inverse

h(x) = ∛ x − 3

​We Do/ Think Pair Share - Find Inverse

g(x) = 7x + 18
2

​We Do/ Think Pair Share - Find Inverse

f (x) = 4x

Function Transformation

A "function transformation" refers to the process of moving a function's graph up, down, left, or right without changing its shape​

​Function Transformation

When determining weather the function is moving up, down, or side to side.

We have Shifts, Stretch's, Reflections and Shrinks.

Stretch's:

F(x)+2 = Vertical Shift up (Positive Sign)

F(x)-3 = Vertical Shift Down (Negative Sign)

F(x-4) = Horizontal Shift to the right (Neg Sign)

F(x+3) = Horizontal Shift to the left (Pos Sign)

Stretch & Shrinks

2F(x) = Vertical Stretch
1/2F(x) = Vertical Shrink
F(2x) = Horzontial Shrink
F(1/2x) = Horzonital Stretch

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​Reflections:
-F(x) = Reflect over X-Axis
F(-x) = Reflect over Y- Axis
-F(-x) = Reflect over the origin

Visual Identification