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: Option D

Step-by-step 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 $b$ the graph moves vertically down

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

If $h$ 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