Question

The functions f(x) and g(x) are described below:

f(x) = 3x − 7
g(x) = 3x + 8

The graph of g(x) is obtained by shifting up the graph of f(x) by _____ units

Answer 1

what do u think the answer is

Answer 2

i think its 8 because it is going up a positive 8

Answer 3

but idk if thats right or if thats how it is supposed to be done

Answer 4

mmmmmmm close but not quite

Answer 5

Okay, Let me give you a better Explanation.:

Shift f(x) up \(15\) units.



More complete answer: We have graphs of the form "y = mx + b", where 'm' is the slope, and 'b' is the y-intercept. It's nice to look at these at x=0 (along the y-axis), and we can start to see how far apart they are. In addition, their 'm's are both 3, so they have the same slope (makes life potentially easier for us.)



When we put in \(x=0, ~f(x)=-7~ g(x)=8\). From there, we can find the difference, or the amount one needs to be shifted to match the other! "\(|-7 - 8| = 15\)" Since we know f(x) is lower, we can then use that to shift up to make g(x).

Answer 6

yep

Answer 7

its 15

Answer 8

15units. The function has y-intercept , The function has y-intercept, If we shift the graph of g(x) up to obtain f(x), then the y-intercept must move from to . This means that the graph will move up by; units.

Answer 9

thank you. all of you

Answer 10

Np

Answer 11

My Pleasure.