Question

The function f(x) passes through the point (-3, 3). If g(x)=f(x-3)+4, then which one of these points, if any, must lie on the graph of g(x)?

Answer 1

\[x-3=-3\\
x=0\]

Answer 2

so if \[f(-3)=3\] then
\[g(0)=f(0-3)+4=3+4\]

Answer 3

wow thats a lot to process ok so then what

Answer 4

add \(3+4\)

Answer 5

it does look confusing, but one thing that should not be confusing is that if
\[(-3,3)\] is on the graph of \(f\) then that measn
\[f(-3)=3\] right?

Answer 6

okay so that means it equals 7.. what then

Answer 7

lets back up

Answer 8

\[g(x)=f(x-3)+4\]

Answer 9

you only know what \(f(-3)\) is

Answer 10

so the only way to know a value for \(g\) is if the input is \(-3\) which will be the case if \(x=0\) since
\[0-3=-3\]

Answer 11

if \(x=0\) then \(g(0)=f(0-3)+4=f(-3)+4=7\)

Answer 12

that means, on the graph of \(g\) is the point \((0,7)\)

Answer 13

okay so how would you do this next one.. i kinda understand. the function f(x) passes through (4,-2). If g(x)=-f(x), which one of these points must lie on graph of g(x)

Answer 14

so if \(f(4)=-2\) the \(g(4)=-f(4)=-(-2)=2\)

Answer 15

which is a long winded way of saying if \((4,-2)\) is on the graph of \(f\) then \((4,2)\) is on the graph of \(-f\)

Answer 16

wow you are a god. okay ill probably have another question soon dont leave meh

Answer 17

ok dear i will stay

Answer 18

not a god however, just a satellite