Question

If the maximum value in the range of the function y=f(x) is 6, what is the maximum value in the range of the function y=3f(x-1)?

Answer 1

either the question is 100% clear
or u said the maximum is 6 , and asked what's the maximum? :\

Answer 2

i know. i left off part of the question sorry

Answer 3

it's okay @Megan2015 , now it's clear ;)

Answer 4

Do you know how to do it? @Ahmad1

Answer 5

for the function f(x-1) let y =x-1 , thus the maximum of function in term of is f(y)=6 since f(x) max=6 , so the maximum of 3*f(y)=3* maxium f(y) =3*6=18

Answer 6

did that make sense ?

Answer 7

not really so the maximum of the function is the maximum of the other function times 3 because there is a coefficient in the second problem?

Answer 8

@Ahmad1

Answer 9

yes , and the trick x-1 instead of x does not effect (if the domain is not restricted)
imagine that the maximum occur at 0 such that f(0)=6
so the maximum in f(x-1) will occur at 1 such that f(1-1)=6 ,
then you multiply by 3

Answer 10

oh ok! thank you!

Answer 11

Another way of putting it is that \(f(x-1)\) is \(f(x)\) shifted horizontally, so the \(x-1\) shouldn't affect the maximum value.

Answer 12

you are welcome

Answer 13

@SithsAndGiggles by shifted do you mean to the left?

Answer 14

For this particular problem the direction of the shift doesn't matter.

But in general, given \(f(x-c)\), this means you have \(f(x)\) shifted to the right by \(c\) units if \(c>0\), or shifted to the left by \(c\) units if \(c<0\).

Answer 15

@SithsAndGiggles okay. that makes sense. but the maximum value still changes right?

Answer 16

No. Here's an example: