Chapter 8, Problem 9CA

a.

To determine

To find: Whether graph is linear or nonlinear function

Answer to Problem 9CA

Graph is a linear function.

Explanation of Solution

Given: Given points on the graph are $(1,45),(2,90),(3,135),(4,180),(5,225),(6,270).$

Calculation: Slope of end points $=\frac{(270-45)}{(6-1)}=45$

Slope of first two points $=\frac{(90-45)}{(2-1)}=45$

In the same manner we can find slope between any two points and we will be getting 45 only.

Therefore slope is same for any two points the graph is linear.

Conclusion:

Given graph is linear function.

b.

To determine

To find: The domain and to find whether domain is continuous or discrete.

Answer to Problem 9CA

Domain is (1,2,3,4,5,6) and it is discrete.

Explanation of Solution

Given: Given points on the graph are $(1,45),(2,90),(3,135),(4,180),(5,225),(6,270).$

Calculation:

Domain is all the $x$ axis values of given points for which function is defined.

Therefore domain is (1,2,3,4,5,6).

We can see the domain set is integers therefore domain is discrete.

c.

To determine

To find: The equation of the function.

Answer to Problem 9CA

Equation of the function is $$

  $y=45x$

Explanation of Solution

Given: Given points on the graph are $(1,45),(2,90),(3,135),(4,180),(5,225),(6,270).$

Calculation:

We already know function is linear and slope is 45 from part a.

Therefore function equation is $\frac{y-45}{x-1}=45$

  $\Rightarrow y=45x$

Conclusion:

Equation of function is $$

  $y=45x$

d.

To determine

To find: whether referee can earn exactly $500

Answer to Problem 9CA

No, he can’t earn exactly $500.

Explanation of Solution

Given:

Function equation is $$

  $y=45x$ from part c.

Calculation:

For referee to earn exactly $500 it should fit in the graph with $x$ an integer.

Therefore by equation $500=45x$

  $x=11.11$

Therefore for $y=500$ x is not an integer.

Therefore referee cannot earn exactly $500.