Question

Let f(x) = 5^x let g(x) = 5^x-7 which statement describes the graph of g(x) with respect to graph of f(x)

Answer 1

Answer: 1. $g(x)$ is translated 7 units down from $f(x)$

Step-by-step explanation:

The missing statements are:

1. $g(x)$ is translated 7 units down from  $f(x)$

2. $g(x)$ is translated 7 units left from  $f(x)$

3. $g(x)$ is translated 7 units up from  $f(x)$

4. $g(x)$ is translated 7 units right from  $f(x)$

Below are shown some transformations for a function  $f(x)$:

If $f(x)+k$, the function is shifted up "k" units.

If $f(x)-k$, the function is shifted down "k" units.

If $f(x+k)$, the function is shifted left "k" units.

If $f(x-k)$, the function is shifted right "k" units.

Then, in this case, given the function  $f(x)$:

$f(x) = 5^x$

And given the function $g(x)$:

$g(x) = 5^x-7$

You can identify the transformation:

$f(x)-k$

Therefore, based on the transformations explained before, you can conclude that the graph of the function $g(x)$ is translated 7 units down from the graph of the  function $f(x)$.