Chapter 1.7, Problem 10CYU

a

To determine

The domain and range of the relation $y=0.13x$ and explain the reason for the relation to be a function.

Answer to Problem 10CYU

Domain: $x\in Z^{+}$

Range: $y\in \{R^{+},$ which are multiple of 0.13}

Explanation of Solution

Given:

The relation is $y=0.13x$

Where x = No. of pictures printed.

y = Cost in dollars.

Now, values of x will constitute the domain for this relation and x is the No. of pictures printed whose possible values can be positive integers only.

Hence, domain of the relation is: $x\in Z^{+}$

Also, depending on the values of x the values of y will be positive real numbers which will be a multiple of 0.13.

Hence, range of the relation is: $y\in \{R^{+},$ which are multiple of 0.13}

When we observe the relation $y=0.13x$ , it is clear that the relation is linear and for every x there will be a unique value of y and if the vertical line test is conducted any vertical line will cut the graph at one point only.

Hence, the relation is a function.

Conclusion:

Therefore, the domain of the relation is $x\in Z^{+}$ and the range of the relation is $y\in \{R^{+},$ which are multiple of 0.13}.

b

To determine

To write the equation in function notation and interpret it

Answer to Problem 10CYU

The function representation of equation is $f(x)=0.13x$

Explanation of Solution

Since the given equation is, $y=0.13x$

In order to obtain the function form of equation substitute y as f(x),

Then the function representation of equation becomes $f(x)=0.13x$

Now if the no. of pages to be printed is 6 which means x = 6

Then, $f(6)=0.13\times 6=0.78$

That means, to print 6 pages, the cost will be 0.78 dollars.

c

To determine

To find $f(5)$ and $f(12)$ .

Answer to Problem 10CYU

  $\begin{array}{l}f(5)=0.65\\ f(12)=1.56\end{array}$

Explanation of Solution

Since the given equation is, $y=0.13x$

Then the function representation of equation becomes $f(x)=0.13x$

Now if the no. of pages to be printed is 5 which means x = 5

Then, $f(5)=0.13\times 5=0.65$

This means that, to print 5 pages the cost will be 0.65 dollars.

Similarly, if the no. of pages to be printed is 12 which means x = 12

Then, $f(12)=0.13\times 12=1.56$

This means that, to print 12 pages the cost will be 1.56 dollars.

Conclusion:

The values are:

  $\begin{array}{l}f(5)=0.65\\ f(12)=1.56\end{array}$