Question

The function AD) defined by the rule AD)=0.140 + 15 represents the cost in dollars of producingacustom textbook that has p pages for college A, where 0

Answer 1

To find the slope of A(p), remember the standard form of a linear function with slope m and y-intercept b:

`y=mx+b`

By comparing with the equation:

`A(p)=0.14p+15`

We know that the slope of A is equal to 0.14.

To find the slope of B(p), use the pairs of data provided by the table. Remember the slope formula:

`m=\frac{B(p_2)-B(p_1)}{p_2-p_1_{}}`

Choose two values of p to find the slope. For example, p=0 and p=50:

`\begin{gathered} m=(B(50)-B(0))/(50-0) \\ =(31-25)/(50-0) \\ =(6)/(50) \\ =0.12 \end{gathered}`

Therefore, the slope of B is equal to 0.12.

Notice that the slope represents the cost per page. Since the slope of A is 0.14 and the slope of B is 0.12, therefore the cost per page is greater for college A than for college B.

The y-intercept is the value of the function when p=0.

From the equation:

`A(0)=15`

And from the table:

`B(0)=25`

Therefore, the y-intercept of A(p) is 15 and the y-intercept of B(p) is 25.

Since the y-intercept represents the initial cost, then, the initial cost is greater for college B than for college A.

The domain is the set of numbers that the function admits. In this case, it is the number of pages p, which can vary in both functions from 0 to 500.

Therefore, the domains of each function are equal, since both can produce up to 500 pages.

To find the range of values of each function, since these are linear functions, evaluate at the endpoints of the domain:

`\begin{gathered} A(0)=15 \\ A(500)=85 \end{gathered}`
`\begin{gathered} B(0)=25 \\ B(500)=85 \end{gathered}`

Therefore, a textbook from college A costs between $15 and $85 while a textbook from college B costs between $25 and $85.