Given that (6,-8) is on the graph of f(x), find the corresponding point for the function f(-1/2x).

Question

jtvatsim · Answer

Hmm... same type again huh? Well, we should have a better chance this time since we got the first one. :)

jtvatsim · Answer

Let's see, all we know is that f(6) = -8. That is "When x = 6, then y = -8". This means I can only get an answer if the x-value on the inside is equal to 6.

anonymous · Answer

Are you going to come back @jtvatsim

jtvatsim · Answer

So, I will force the inside of f(-1/2x) to be equal to 6. How can I do this?

Easy, I wish for -1/2x = 6, so I can have my wish if x = -12. You can check that this actually works.

So, we just have
f(-1/2 * -12) = f(6) = -8.

The corresponding point is x = -12, then y = -8. (-12,-8)

anonymous · Answer

@jtvatsim Thank you so much. I understand what to do now, and I just answered and got one correct on my own.  Cheers

jtvatsim · Answer

Any questions? It's a little weird. 

My gut instinct when first doing this problem was just to plug in the original x-value like x = 6. But, I realized that this was a dead end, cuz we get 

f(-1/2 * 6) = f(-3)

and I have no idea what f(-3) is supposed to equal...

So, if we are more clever, we'll realize that we need to choose our x-value so that we END UP WITH the inside equal to 6. This is why I pick x = -12. Because then,

f(-1/2 * -12) = f(6)

and I know exactly what that equals, f(6) = -8.

jtvatsim · Answer

Awesome! Congrats! They aren't easy, so be proud of that! :)