Question

Which statement is true about the effects of the transformations on the graph of function f to obtain the graph of function g.

g(x) = f(x - 3) + 4


A. The graph of function f is shifted right 3 units and down 4 units.

B. The graph of function f is shifted left 3 units and down 4 units.

C. The graph of function f is shifted left 3 units and up 4 units.

D. The graph of function f is shifted right 3 units and up 4 units.

Answer 1

D

Explanation:

Because its shifted right 3

because when its inside the sign changes. like if its +4 its going left/-4 going right if its inside only

Answer 2

The graph of function f is shifted right 3 units and up 4 units.

Explanation:

Let f(x) be the parent function.

Rule : f(x)→f(x-b)

The graph shifts right by b units

So, shift the parent graph by 3 units

So, f(x)→f(x-3)

So, the graph shifted right by 3 units

Rule : f(x)→f(x)+b

The graph shifts up by b units

Now shift the obtained graph up by 4 units

So, f(x-3)→f(x-3)+4

So, the graph shifts up by 4 units

Thus Option D is correct.

The graph of function f is shifted right 3 units and up 4 units.

So, g(x) = f(x-3)+4

Thus