Question

If the range of the functions y=f(x) is all real numbers between -1 and 12, inclusive, then what is the maximum value of g(x) if g(x)=2f(x-1)+3?

Answer 1

What's the highest value that f(x-1) could be?

Answer 2

I think that's my problem. I only know the highest value for f(x)

Answer 3

When it comes to minimum/maximum outputs, all that matters is which function we're talking about. f(x), f(x-1), f(3x+2) and f(x²) would all have the same minimum and maximum outputs, just at different inputs.

Answer 4

But the range is -1<=y<=12 for f(x). If it is for f(x-1), would the graph be shifted and thus the range for f(x-1) different?

Answer 5

For f(x-1), the graph would be shifted, but in the x direction ONLY. So, the range of y values would not be affected, The only difference would be the x location of the max/min

Answer 6

Isn't this how it would be, though? f(x)!=f(x-1)