Given the following transformations 𝑦 = 3𝑓(−2𝑥 + 8) − 6 to the parent function 𝑓(𝑥) = 𝑙𝑜𝑔2(𝑥), describe (in words) how to determine the following key features of the transformed function without graphing:

Question

Domain:
Range:
x-Int:
y-int:
Asymptotes:

I'm having a lot of trouble with the x-int for this one. Can't decide whether it's (2, 0) or (3.5, 0).

Answer 1

since log(1) = 0
you want -2x+8 = 1
x = 7/2

Answer 2

Thanks buddy! But I just want to make sure: how come you're not just subbing 0 into the equation to make the x-intercept 2?

Also if you graph 𝑦 = 3log2(−2𝑥 + 8) − 6 on demos, the x-int is 2. What's up with that?

Answer 3

Really sorry to bother everyone but is the y-intercept (0, 3)?