Question

The graph of g(x) is obtained by reflecting the graph of f(x)=4|x| over the x-axis.

Which equation describes g(x)?

A) g(x)=|x−4|

B) g(x)=|x+4|

C) g(x)=−4|x|

D) g(x)=|x|−4

Answer 1

That would be choice C.

The graph of  4|x| is shaped like a V whose vertex is at the origin.

Every y value will be positive for y = 4|x|  as |x| is always positive  and a reflection in the x axis will make every y value negative.

Answer 2

Through moving up c units, the graphs of g can be determined from the graph of f. If we subtract c from f(x), the graph shifts downward. Let $\bold{ h(x) = f(x) - c}$. Shifting downward c units yields this graph of h from the graph of f.

Given:

$\bold{f(x)=4|x|}$

Calculation:

• It is stated that its graph of $g(x)$ is obtained by reflecting a graph of $f(x)=4|x|$ over the x-axis.

• When a figure is reflected across the x-axis, the rule for reflection is $\bold{(x,y) \to (x,-y)}$.

• To use the preceding logic, if the given function is reflected from across the x-axis, then $g(x)=-f (x)$.

           $\bold{g(x)=-(4|x|)}\\\\\bold{g(x)=-4|x|}$

So, the equation $g(x)=-4|x|$ describes $g(x)$.

Therefore, the final choice is "Option C".

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