Question

Suppose that the graph of f contains the point (4,5). Find a point that must be on the graph of g(x)=2+f(x)

Answer 1

Hint:

if (4,5) is on the graph, then f(4) = 5

Answer 2

still need help?

Answer 3

yes please!

Answer 4

do you understand jim thompsons' hint?

Answer 5

Try finding g(4)

Answer 6

No, I am confused about it.

Answer 7

since g(x)=2+f(x), then
g(4) = 2 + f(4) = ??

Answer 8

Oh...shoot. My apologies I wrote my the equation wrong. It's supposed to be g(x)=2+f(6x)

Answer 9

jim??? all your bud... :)

Answer 10

*yours

Answer 11

the only thing you know is that f(4) = 5

so you're stuck with f(4)...but when x = 4, f(6x) = f(6*4) = f(24)...which is in uncharted territory and we have no idea what it is (if it even exists)

but

you can force f(6x) to be f(4) like so

6x = 4

x = 4/6

x = 2/3

So because x = 2/3 satisfies 6x = 4, we know for a fact that f(6x) = f(4) when x = 2/3

but we also know that f(4) = 5

so this means

g(x) = 2 + f(6x)

g(2/3) = 2 + f(6*2/3)

g(2/3) = 2 + f(4)

g(2/3) = 2 + 5

g(2/3) = 7

So the point (2/3, 7) must be on the graph of g(x) = 2 + f(6x) given that (4,5) is on the graph of f(x)

Answer 12

Thank you so much!