Chapter 8.4, Problem 38PPS

a.

To determine

To graph:

The given function

Explanation of Solution

Given information:

Alana plays softball and so far this season she has gotten a hit 4 out of 12 times at bat.

The function for Alana’s batting average is $B\left(x\right)=\frac{4+x}{12+x}$ if she can get $x$ consecutive hits

Graph:

  

Interpretation:

The given function is plotted in the graphing calculator and the graph is obtained.

b.

To determine

To explain what part of the graph is meaningful in the context of the problem

Answer to Problem 38PPS

The meaningful part of the graph in context of the problem is first quadrant because $x$ that is a positive number represents the number of consecutive hits

Explanation of Solution

Given information:

Alana plays softball and so far this season she has gotten a hit 4 out of 12 times at bat.

The function for Alana’s batting average is $B\left(x\right)=\frac{4+x}{12+x}$ if she can get $x$ consecutive hits

The first quadrant of the graph will be meaningful when the consecutive hits on the bat is positive number.

Here, $x$ represents the number of consecutive hits and it is a positive number. Thus, the part of the graph that is meaningful is the one in the first quadrant.

c.

To determine

To describe the meaning of the intercepts of the vertical axis

Answer to Problem 38PPS

The intercepts of the vertical axis means Alana’s batting average now, before her next $x$ hits

Explanation of Solution

Given information:

Alana plays softball and so far this season she has gotten a hit 4 out of 12 times at bat.

The function for Alana’s batting average is $B\left(x\right)=\frac{4+x}{12+x}$ if she can get $x$ consecutive hits

In an analytical geometry, the vertical axis represents a variable $y$ , a $y$ -intercept or vertical intercept is a point where the graph of a function or relation intersects the $y$ -axis of the coordinate system.

Therefore, here vertical intercepts represent Alana’s batting average now, before her next $x$ hits

d.

To determine

To write the equation of horizontal asymptote and also explain its meaning with respect Alana’s batting average

Answer to Problem 38PPS

The equation of horizontal asymptote is $y=1$ which means Alana’s batting average will never reach nor exceed 100% because of her initial performance of hitting 4 out of 12 at hits

Explanation of Solution

Given information:

Alana plays softball and so far this season she has gotten a hit 4 out of 12 times at bat.

The function for Alana’s batting average is $B\left(x\right)=\frac{4+x}{12+x}$ if she can get $x$ consecutive hits

To find the horizontal asymptote divide numerator’s leading co-efficient from denominator leading co-efficient,

  $\begin{array}{l}y=\frac{\text{numerator's leading coefficient}}{\text{denominator's leading coefficient}}\\ y=\frac{1}{1}=1\end{array}$

Therefore, the horizontal asymptote is $y=1$

Since the function represents Alana’s batting average, then $y=1$ means 100%

This means that Alana’s batting average will never reach nor exceed 100% because of her initial performance of hitting 4 out of 12 at hits