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