Functions

Algebra: Functions

Read the following SAT test question and then select the correct answer.

Read each question carefully and identify the bottom line to avoid making careless mistakes.  Then assess your options and choose the most efficient method to attack the problem.  When you have an answer, loop back to verify that it matches the bottom line.

If f(x) = x + ax, and $a =\frac{7}{2}$ what is $f(\frac{3}{2})$?

Bottom Line$f(\frac{3}{2})=?$

Assess your Options:  You could use your graphing calculator to solve this problem, but it would probably take you more time to type in the fractions than to just solve the problem.  You are given a value for each variable in the problem so all you need to do is plug them in.

Attack the Problem:  Start by plugging in the value of a to the function that you were given.

$f(x)=x+ax$
$f(x)=x+\frac{7}{2}x$

Simplify the problem by adding.  Remember that the first x is a whole 1x, but that you must have like terms before you can add fractions.

$f(x)=\frac{2}{2}x+\frac{7}{2}x$
$f(x)=\frac{9}{2}x$

Now solve your function by plugging in the value for x that you were given.

$f(\frac{3}{2})=(\frac{9}{2}\)(\frac{3}{2})$
$f(\frac{3}{2})=\frac{27}{4}$

Loop Back:  You found your bottom line, so you are ready to look down at the answer choices.

(A) $\frac{1}{3}$
(B) $\frac{3}{2}$
(C) $\frac{7}{2}$
(D)$\frac{21}{4}$
(E) $\frac{27}{4}$