Question

Which of the following statements best describes the effect of replacing the graph of f(x) with the graph of f(x) - 5?

a. The graph shifts 5 units up.
b. The graph shifts 5 units down.
c. The graph shifts 5 units left.
d. The graph shifts 5 units right.

Answer 1

The statement which best describes the effect of replacing the graph of f(x) with the graph of f(x) - 5 is:

b. The graph shifts 5 units down.

Explanation:

We know that the transformation of the type:

f(x) → f(x)+k

is a translation transformation that shifts the original function f(x) either k units up or k units down depending on k.

If k>0 then the shift is k units up.

and if k<0 then the shift is k units down.

Here we have: k= -5<0

Hence, the shift is 5 units down.

( Let us assume:

f(x)=x² (red curve)

then f(x)-5=x²-5 (blue curve)

we may observe from the graph that there is a shift of 5 units down )

Answer 2

The correct answer among the choices given is option C. The graph is shifted 5 units to the left if the graph of f(x) is replaced with the graph of f(x) -5. f(x) represents something as a function of x this means that it is dependent with changes in x so when you subtract -5 it changed the value of the whole function.