The point (-14,3) is on the graph of y=f(x). Find the corresponding point on the graph of y=1/3f(x). The corresponding point on the graph of y=g(x) is what?

Answer 1

Hi Mackenzie B.,

The corresponding point on the graph of y=g(x) is (-14,1). Before I explain how I approached this problem, you have to keep in mind that y=g(x) is the same thing as y = 1/3*f(x).

With this in mind, lets begin the problem!

Since the change in the graph [from y=f(x) to y=1/3*f(x)] is affecting the y-variable, the only part of the corresponding point that is changed is the y-variable. Thus, we can just plug the x value of the point (-14) into the new function y=1/3*f(x). This results in y=1/3*f(-14) or y=1/3*(3) since we already know that f(-14) = 3. Simplifying y=1/3*3 results in 1. Thus the corresponding point is (-14,1)

In fact, any value of x that is inserted, the corresponding y-value will always be 1/3 of the original y-value!

Feel free to ask me more if you are still confused!

I hope this helps :)

Manu

Answer 2

If (-14,3) is on a graph y=f(x), that means f(-14)=3. If we multiply f(x)by 1/3, all the y coordinates are divided by 3, since y=f(x). From that we see (1/3)f(-14)=1, making the corresponding point (-14,1).

We need to know what g(x) is to see what the corresponding point on that graph is.