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.
Now we will draw the inverse. Push 2nd and PRGM. In the DRAW menu, scroll down and select 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.
Notice that the original function is in vertex form. Let's highlight the coefficients. y=(x-3)^2 ⇔ y= 1(x+(- 3))^2 + 0 We conclude that (- 3,0) is the vertex. To sketch the function, we should find two more points that belong to its graph. We are going to do that by substituting 1 and 5 for x into the function rule.
We found that (1,4) is one of the points. Let's find the other.
Another point on the graph is (5,4). Now we have what we need to sketch the original function. We are going to do that by plotting, then connecting the points with a smooth line. Notice that the inverse function is the original function rotated 90^(∘) to the right, whilst the coordinates of the points are reversed.
