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.

List of Operations and Inverses.

Identify Correct Inverses.

​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

​

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

Visual Identification