Answer:
The answer figure is attached in this answer.
Step-by-step explanation:
The graph shows that [tex]y[/tex] always has positive value whether [tex]x[/tex] is positive or negative. Following observations can be drawn from the question figure.
- When [tex]x[/tex] is 0, [tex]y[/tex] is also 0.
- When [tex]x[/tex] is 1, [tex]y[/tex] is 2.
- when [tex]x[/tex] is 2, [tex]y[/tex] is 4.
- when [tex]x[/tex] is -1, [tex]y[/tex] is 2.
- when [tex]x[/tex] is -2, [tex]y[/tex] is 4.
It means [tex]f(x)[/tex] is a function of modulus function (|[tex]x[/tex]|).
Let us provide definition of modulus function [tex]g(x)[/tex]:
[tex]g(x) = |x|=\left \{ {{x, \ if\ x \geq0 } \atop {-x,\ if \ x < 0}} \right.[/tex]
As we can observe that [tex]y[/tex]is twice of |[tex]x[/tex]|, so the graph given in the question figure represents
[tex]y= f(x) = 2|x| \{ {-2\leq x}\leq 2 \}[/tex]
So, we have to draw the graph of [tex]y = \dfrac {1}{2} f(x)[/tex]
i.e. [tex]y = |x| \{-2\leq x \leq 2 \}[/tex]
Please refer to the attached figure for the graph of [tex]y = \dfrac {1}{2} f(x)[/tex]
