Question

If the graph of function g is 6 units below the graph of function f, which could be function g? f(x) = -2x + 7 A. g(x) = -2x + 1 B. g(x) = -2x − 6 C. g(x) = -6x + 7 D. g(x) = -2x + 20

Answer 1

Answer:

A. $g(x)=-2x+1$

Step-by-step explanation:

Given:

$f(x)=-2x+7$

The function $f(x)$ is shifted 6 units below which forms the function $g(x)$

To find the function $g(x)$, we apply the following translation rules:

$f(x)\rightarrow f(x)+c$

If $c>0$ the function $f(x)$ shifts $c$ units up.

If $c$ the function $f(x)$ shifts $c$ units down.

Since the function $f(x)$ is shifting 6 units below, thus value of $c$ which is taken as  -6.

The translation occurring here is given by:

$f(x)\rightarrow f(x)-6$

Thus,

$g(x)=f(x)-6$

Substituting $f(x)=-2x+7$

$g(x)=-2x+7-6$

∴ $g(x)=-2x+1$