Macioccujx

2022-07-25

Find the coordinates of a second point on the graph of afunction f if the given point is on the graph and the function is(a) even and (b) odd.
1) (-3/2,4)
2) (4,9)

polishxcore5z

Expert

You have two points of the form (x,y).
1. (-3/2,4) means that f(x) = f(-3/2) = 4
2. (4,9) means that f(x) = f(4) = 9
If a function f(x) is even then f(-x) = f(x), meaning that if youplug in -x you get y.
Example: $f\left(x\right)={x}^{2}$ is even because $f\left(-x\right)=\left(-x{\right)}^{2}={x}^{2}$
So if a function is even, you can plug in (-x) and you get the sameanswer as when you plugged in x.
So in your example if f is even you get the same y value for -3/2as well as positive 3/2.
If f(x) is odd the f(-x) = -f(x) meaning that when you plug in -xyou will get -y.

Do you have a similar question?