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Stretching Functions Vertically

You can also change the graphs shapes along with shifting the graph.

-You can change the shape of the graph by just adding a number by adding it to the front of the function. For example, your graph is F(x)=x^3-3x; lets say you want to stretch the factor by two, you multiply it by two. G(x)=2x^3-6x.

Shifting to the Left or Right

If you want to shift the function left you its a little bit different. Lets say that the graph you are trying to shift is G(x)=x^3. you want to shift it 2 units to the left, you add (+2). so the function becomes G(x)=(x+2)^3. and lets say you want to move it twice to the right, its the same process but instead you subtract two. so the function is G(x)=(x-2)^3

Shifting Functions

The graph of an inverse can also be shifted in any way. It can be moved up, down, left, and right.

For a function to move up, you have to add the amount to the end, For Example: Shift the graph of G(x)=x^2 five units up, you just add +5 to the end of the function; G(x)=x^2+5.

and if you want to shift down, you just have to -5 so it would be G(x)=x^2-5

Undoing Functions and Moving Them Around

Section 4

Graphs of Inverses

In this section we learn how to tell if a graph of an inverse is a function.

-One of the most important and easiest ways to find out if an inverse is a function, is called the

Horizontal line test.

- If any horizontal line intersects the graph in more than one point, the inverse is not a function.

Examples of Inverse Function

Find the inverse function of F(x)=x+2?

1)Rewrite the function. y=x+2

2)Switch the (x) and (y). x=y+2

3)Subtract 2 from both sides. x-2=y

4)Flip the function y=x-2

5)Switch the (x) and (y). x=y-2

6)Final answer is [F^-1(y)=y-2]

Inverse Ordered Pairs

Here is a mapping diagram of a function that takes letters as inputs and returns them in letters as outputs

By

Christian Chavez

The ordered pairs are:

(A,0) (B,1) (B,-1), etc.

The ordered pairs for its

inverse are:

(0,A) (1,B) (-1,B), etc.

Inverses

  • An inverse function is a function that "reverses" another function: if the function (F) applied to an input (x) gives a result of (y), then applying its inverse function (G) to (y) gives the result (x).
  • F(x) = y, if and only if, G(y) = x
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