Question

What transformations change the graph of f(x) to the graph of g(x)?

f(x)=x^2
g(x)=(x+3)^2-7

Answer 1

B. The graph of g is the graph of f translated to the left 3 units and down 7 units.

Explanation:

f(x) = x² to g(x) = (x + 3)² - 7

Notice the difference:

from 'x' to 'x + 3'

and then from 'x²' to '(x+3)² - 7'

The transformation that changes 'x' to 'x + 3' is the translation across the x-axis, three units to the left. The transformation that changes 'x²' to (x + 3)² - 7' is the translation across the y-axis, seven unit down. Refer to the graph attached below to visualize the transformation. Take the vertex of f(x) = x² and translate it three unit left and seven unit down to get g(x).

Answer 2

f(x) = x² to g(x) = (x + 3)² - 7

Notice the difference:
from 'x' to 'x + 3'
and then from 'x²' to '(x+3)² - 7'

The transformation that changes 'x' to 'x + 3' is the translation across the x-axis, three units to the left

The transformation that changes 'x²' to (x + 3)² - 7' is the translation across the y-axis, seven unit down

Refer to the graph attached below to visualize the transformation. Take the vertex of f(x) = x² and translate it three unit left and seven unit down to get g(x).