Question

The graph of f(x) = x2 is shifted 3 units to the left to obtain the graph of g(x). Which of the following equations best describes g(x)?

Answer 1

@jim_thompson5910

Answer 2

by x2 I meant x^2

Answer 3

to shift to the left, change
\[f(x)\] in to \(f(x+3)\)

Answer 4

why +3 if we are going left, aka minus?

Answer 5

the "it" is the graph, not the input

Answer 6

what is really happening is the y axis is shifting 3 units to the right, which makes the graph appear to shift 3 units to the left
lets do an example

Answer 7

ok

Answer 8

I remember this... precalc stuff... but yeah anything in the parenthesis indicates left or right. without it you will be going up or down. Like for example f(x) = x^2+3 I am going up 3 units... f(x)=x^2-3 I'm going down 3 units

Answer 9

we can even do it with \(f(x)=x^2\) that graph has the following ordered pairs
\[\{-4,16),(-3,9),(-2,4),(-1,1),(0,0),(1,1),(2,4)\] and so on
now lets take a look at the ordered pairs for \(f(x+3)=(x+3)^2\) and plug on those same numbers

Answer 10

f(x) = (x^2-3) I'm going 3 units to the right.
f(x) =(x^2+3) I'm going 3 units to the left

so what you do is you graph your x^2 and then shift it according to the directions.

Answer 11

\[(-4,1),(-3,0),(-2,1),(-1,4),(0,9), (1,16)\] and so on
`

Answer 12

you are adding the 3 FIRST then evaluation the function
it has the effect or translating the graph to the LEFT 3 units

Answer 13

ok ok... im following so far... could the answer possibly be g(x) = (x + 3)^2?

Answer 14

yes

Answer 15

thanks for helping both of you, I immediatly understood what to do after your help :D

Answer 16

yw