Write an equation to construct a function whose graph is like that of y=x^2, except for pieces removed for values between 3 and 5, and 8 and 9.

I am not sure how to approach this question. Would I make a piece wise function? PLease helpp brains about to explode!

Wouldn't you just include the following domain for x,

x ≤ 3 OR 5≤x≤8 OR x ≥ 9 ?

something like

f(x) = x^2, x ≤ 3 OR 5≤x≤8 OR x ≥ 9

You don't say what happens to the function for the restricted values of x, so it would be just a discontinuous function I suppose.

To construct a function whose graph is like that of y=x^2, except for the pieces removed for values between 3 and 5, and 8 and 9, you can indeed use a piecewise function.

A piecewise function is a function that is defined by different equations over different intervals. In this case, we'll define different equations for different intervals to remove the desired pieces from the graph.

Let's break it down step by step:

1. Define the equation for the part of the graph that is not removed (y=x^2):
f(x) = x^2

2. Define the equation for the pieces removed from the graph:

(a) For values between 3 and 5:
Remove the values between 3 and 5 by setting the equation to zero:
f(x) = 0 for 3 ≤ x ≤ 5

(b) For values between 8 and 9:
Remove the values between 8 and 9 by setting the equation to zero:
f(x) = 0 for 8 ≤ x ≤ 9

3. Combine these equations to create the piecewise function:

f(x) = {
x^2 if x ≤ 3 or x ≥ 9
0 if 3 < x < 5 or 8 < x < 9
}

The piecewise function defined above will have a graph similar to y=x^2, but with the pieces removed for values between 3 and 5, and 8 and 9.