Chapter 1.7, Problem 69E

(a)

To determine

To find: The graph for the function.

Explanation of Solution

Given:

The expression for the required horse power is $0.002x^2+0.005x-0.02910\le x\le 100$ .

Calculation:

Consider the given function is,

  $Y_1=0.002x^2+0.005x-0.029$

Input the above expression in the calculator as,

The sketch for the input values is shown in Figure 1

  

Figure 1

Then, press the graph key and the graph of the function obtained is shown in Figure 2

  

Figure 2

(b)

To determine

To find: The horsepower function such that the $x$ represents the speed in kilometre per hour. Then determine $H\left(\frac{x}{1.6}\right)$ and then find the type transformation applied to the graph of the horsepower function.

Answer to Problem 69E

The required transformation is $H\left(\frac{x}{1.6}\right)=0.00078x^2+0.003x-0.029$ and the transformation applied is horizontal.

Explanation of Solution

Given:

The expression for the required horse power is $0.002x^2+0.005x-0.02910\le x\le 100$ .

Calculation:

The horsepower function such that the $x$ is the speed limit in kilometre per hour and substitute $\frac{x}{1.6}$ for $x$ .

  $\begin{array}{c}H\left(\frac{x}{1.6}\right)=0.002x^2+0.005x-0.029\\ =0.002\left(\frac{x^2}{2.56}\right)+0.005\left(\frac{x}{1.6}\right)-0.029\\ =0.00078x^2+0.003x-0.029\end{array}$

The transformation applied to the graph of the horsepower function is horizontal.