Question

The graph of y=f(x) is shown below. Graph y=1/2f(x)

Answer 1

Answer:

The answer figure is attached in this answer.

Step-by-step explanation:

The graph shows that $y$ always has positive value whether $x$ is positive or negative.  Following observations can be drawn from the question figure.

• When $x$ is 0, $y$ is also 0.
• When $x$ is 1, $y$ is 2.
• when $x$ is 2, $y$ is 4.
• when $x$ is -1, $y$ is 2.
• when $x$ is -2, $y$ is 4.

It means $f(x)$ is a function of modulus function (|$x$|).

Let us provide definition of modulus function $g(x)$:

$g(x) = |x|=\left \{ {{x, \ if\ x \geq0 } \atop {-x,\ if \ x < 0}} \right.$

As we can observe that $y$is twice of |$x$|, so the graph given in the question figure represents  

$y= f(x) = 2|x| \{ {-2\leq x}\leq 2 \}$

So, we have to draw the graph of $y = \dfrac {1}{2} f(x)$

i.e. $y = |x| \{-2\leq x \leq 2 \}$

Please refer to the attached figure for the graph of $y = \dfrac {1}{2} f(x)$