Pearson Algebra 2 Common Core, 2011
PA
Pearson Algebra 2 Common Core, 2011 View details
Concept Byte: Graphing Inverses
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Exercise 1 Page 413

The inverse of a function can be viewed as a rotation 90^(∘) to the right.

Graphing Calculator:

Window with a graph

Sketch:

Practice makes perfect

To draw the graph of a function on the calculator, we first have to press Y= and write the function in one of the rows. Having written the function, we push GRAPH to see it.

Fönster med funktioner
Window with a graph

Drawing the Inverse

To draw the inverse we push MODE and change Func to Par.

Window with a graph

Now we will draw the inverse. Push 2nd and PRGM. In the DRAW menu, scroll down and select DrawInv.

Window with a graph
Window with a graph

Be careful to choose the correct function. We typed our function in the first line so we need to choose Y_1. Push VARS and go to the second menu, Y-VARS. Here we select the first option, Function, and then choose Y_1 by pushing ENTER.

Window with a graph
Window with a graph
Window with a graph

If we push ENTER one more time, the inverse function will be drawn on top of the original function.

Window with a graph

Sketching the Graphs

To sketch the graphs, we should find the zeros and y-intercepts of the functions. The original function has a y-intercept of - 5. To find the zeros, we equate the function with 0 and solve for x.
y=x^2-5
0=x^2-5
Solve for x
5=x^2
x^2=5
x=± 2.236
Now we have what we need to sketch the original function. Notice that the inverse function is the original function rotated 90^(∘) to the right. Therefore, it must have an x-intercept of 0 and y-intercepts of ± 2.236. With this information, we have enough to sketch the inverse function as well.