Question

Find the function which closely describes the given graph.

• A.
• B.
• C.
• D.

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A

B

C

D

We will try to define the function, using its graph.

$x>0\Rightarrow f\left(x\right)=1$

$x=0\Rightarrow f\left(x\right)=0$

$x<0\Rightarrow f\left(x\right)=-1$

Combine these three, we get

$f\left(x\right)=\{\begin{array}{cc}1& \text{text{if } xgt 0}\\ 0& \text{text{if } x=0}\\ -1& \text{text{if } xlt 0}\end{array}$

so option D is correct.

Other options are zero when x=0.

$Ifx$ $<$ 0,$\frac{|x|}{x}=\frac{-x}{x}=-1$

$\frac{|x|}{x}=\frac{x}{-x}=-1$

$Ifx$ $>$ 0,$\frac{|x|}{x}=\frac{x}{x}=1$

$\frac{|x|}{x}=\frac{x}{x}=1$

This means A,B and C are equal to the function given in D.

$\Rightarrow$ All the option are correct.