Chapter 4.4, Problem 36PPE

To determine

To select the correct option: The equation of graph

  

is

  

Answer to Problem 36PPE

The correct option is (B).

Explanation of Solution

Given information :

Given graph

  

As we can observe from above graph, the $x-\text{intercept}\text{is}2\text{and}\text{the}y-\text{intercept}\text{is}-1$ reaches maximum and then decreases slowly.

Thus, the equation $y=\frac{1}{2}x-1$ has $x-\text{intercept}\text{is}2\text{and}\text{the}y-\text{intercept}\text{is}-1$ .

Because when $y=0,0=\frac{1}{2}x-1\Rightarrow \frac{1}{2}x=1\Rightarrow x=2$ and when $x=0,y=-1$ .

However, the equation $y=\left|\frac{1}{2}x\right|-1$ has also $x-\text{intercept}\text{is}2\text{and}\text{the}y-\text{intercept}\text{is}-1$ but its graph is not a straight line on its entire domain.

So, the graph of given equation is $y=\frac{1}{2}x-1$ .

Hence, the correct option is (B).