Question

Kaleb incorrectly determined the inverse of y=4− −x

​
to be y=−(x−4) 2
and used the graphing calculator to obtain a parabola. Explain why the graph of the correct inverse is not a complete parabola.

Answer 1

Kaleb's inverse is incorrect due to a mistake in swapping 'x' and 'y'. The correct inverse of y=4-x is y=x-4, which is a straight line, not a parabola.

Step-by-step explanation:

The topic is about the correct inverse of a function. Kaleb's mistake in determining the inverse of y=4-x is because he failed to correctly switch the 'x' and 'y' then solve for 'y'. As a result, he mistakenly found the inverse to be y=- (x-4)^2 which gives him a parabola graph.

The correct inverse of y=4-x should be y=x-4 when you switch 'x' and 'y'. It's important to note that the graph of a correct inverse function reflects the original function across the line y=x. Since the original function was a straight line, its inverse should also be a straight line not a complete parabola.

Learn more about Inverse of a function