Concept Byte: Graphing Inverses
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The inverse of a function can be viewed as a rotation 90^(∘) to the right.
Graphing Calculator:
Sketch:
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.
To draw the inverse we push MODE and change Func
to Par.
DrawInv.
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.
If we push ENTER one more time, the inverse function will be drawn on top of the original function.
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.
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.
