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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.

Respuesta :

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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.

Answer:

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.

Step-by-step 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 )

Ver imagen lidaralbany

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