Question

Each statement describes a transformation of the graph of f(x) = 5x. Which statement correctly describes the graph of g(x) = 5(x + 3) - 7?

Answer 1

Answer: B. It is the graph of f translated 7 units down and 3 units to the right.

Answer 2

Answer: Option D

Explanation:

If the graph of the function
`g(x)=f(x+h) +b` represents the transformations made to the graph of
`y= f(x)` then, by definition:

If
`b> 0` the graph moves vertically upwards.

If
`b <0` the graph moves vertically down

If
`h>0` The graph moves horizontally h units to the left

If
`h<0` The graph moves horizontally h units to the right

In this problem we have the function
`g(x) = 5^((x + 3)) - 7` and our parent function is
`f(x) = 5^x`

therefore it is true that
`h =3>0` and
`b =-7 < 0`

Therefore the graph of
`g(x) = 5^((x + 3)) - 7` is moves horizontally 3 units to the left. Also, as
`b =-7 < 0` then the graph moves vertically 7 units down

Therefore the answer is the option D