Chapter 1, Problem 78CR

To determine

To sketch:

The graph, represented by given equation, $g\left(x\right)=9x+45$ and also to find its domain and range.

Answer to Problem 78CR

Domain is $\{0,1,2,3,4,5,6\}$ and range is $\{45,54,63,72,81,90,99\}$

Explanation of Solution

Given information:

After three quarters, O had rushed 45 yards. If O averaged 9 yards per carry in the fourth quarter and there is enough time to run 6 more plays before the end of the game, the equation $g\left(x\right)=9x+45$ represents the situation.

Concept used:

To first calculate few coordinates to plot in XY plane in ordered pair form $(x,y)$ so that its graph will be a straight line and domain is the set of all x values and range is the set of all $g(x)$ values.

Calculation:

Few coordinates in tabular form are:

x	$g\left(x\right)=9x+45$	$(x,g\left(x\right))$
1	$g\left(1\right)=9\left(1\right)+45=54$	$(1,54)$
2	$g\left(2\right)=9\left(2\right)+45=63$	$(2,63)$

Graph:

In XY plane, seeds are taken on x axis and plants growing on y axis, its graph looks as:

Interpretation:

Also, as numbers of carries may be up to 6 and its range will be total yards occupied in each carry, starting from 45 yards.

Conclusion:

So, the domain as the set of number of carries is $\{0,1,2,3,4,5,6\}$ and the range as a set of all yards occupied be $\{45,54,63,72,81,90,99\}$ .