Question

5. what’s the transformations change the graph of f(x) to the graph of g(x)?

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

A) the graph of g is the graph of f translated the the right 3 units and up 7 units.

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

C) the graph of g is the graph f translated up 3 units and the the left 7 units

D) the graph of g is the graph f translated down 3 units and to the right 7 units.

Answer 1

B

Explanation:

Given f(x) then f(x + a) is a horizontal translation of f(x)

• If a > 0 then a shift to the left of a units

• If a < 0 then a shift to the right of a units

Given f(x) then f(x) + c is a vertical translation of f(x)

• If c > 0 then a shift up of c units

• If c < 0 then a shift down of c units

Given

f(x) = x², then

g(x) = (x + 3)² - 7

is a shift to the left of 3 units and down 7 units → B