Chapter 11, Problem 1STP

To determine

To evaluate: the correct options out of the given options.

Answer to Problem 1STP

Only statement II is true and option B is correct.

Explanation of Solution

Given:

  

The graph of f is shown above.

Statements are given as,

I. The graph of $g\left(x\right)=x-1$ is perpendicular to the graph of f .

II. The y -intercept of the graph of f is (0, 3).

III. The slope of the graph of f is −4.

In this, finding the slope of the f,

Taking the two points from the graph,

  $\left(4,0\right)$ and $\left(0,3\right)$

Finding its slope,

  $\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{3-0}{0-4}\\ =-\frac{3}{4}\end{array}$

Now, it is known that if two lines are perpendicular, then the product of their slopes is −1.

The slope of line given as $g\left(x\right)=x-1$ is 1.

So it can be seen that their product is not −1.

Hence, the lines are not perpendicular and statement I is not true.

Now taking statement II,

Yes it is correct as it can be seen from the graph that y -intercept is (0, 3).

Statement II is true.

Now taking statement III,

The slope is being calculated in the statement I, which is $-\frac{3}{4}$ .

So, it is clear that statement III is false.

Hence, only statement II is true and option B is correct.