Question

Evaluate the function f(p) = p2 + 3p + 1 for p = -2.

A. 1
B. -1
C. -8
D. 9
E. -9

Answer 1

A function is simply a rule that tells you how to associate every (feasible) input with its correspondant output. So, in this case, your function/rule of association is

`\displaystyle f(p) = p^2+3p+1`

which can be read as:

"Given any number
`\displaystyle p`, the correspondant output is that same number squared, plus three times that number itself, plus one".

This rule holds for every possible input
`\displaystyle p`, and of course the result will change depending on which input you will feed the function.

In this case, we're interested in feeding the function the number
`\displaystyle -2`. Let's use the verbose definition first, to understand better what's happening. It translates to

"Given the input
`\displaystyle -2`, the correspondant output is negative two squared, plus three times negative two, plus one".

Which, in formula, is written as

`\displaystyle f(-2) = (-2)^2 + 3(-2) + 1 = 4-6+1 = -1`

Answer 2

f(p) = p^2 + 3p + 1 for p = -2

Substitute p = -2 into f(p) = p^2 + 3p + 1

f(-2) = (-2)^2 + 3(-2) + 1

= 4 - 6 + 1

= -1

Answer

B. -1