How to Solve Function Questions on the SAT

When you read the word “function,” did your heart skip a beat? Perhaps your hair stood up on end a little bit? If so, don’t worry – you are not alone! A lot of students find that function questions are some of their least favorite SAT math questions.  In this 3-part article series, I will try to help you feel better about functions by breaking down the most common types of function questions and giving you some tips on each one. So, without further ado….

The Standard “f(x) = 50x – 25” question type

These questions are often, though not always, word problems. The problem will define a function for you and ask for value of the function at a given x-value, or the x-value for which the function attains a given value.

Remember that function notation, f(x) is another way of writing “y=…”.  The value of the function, or the f(x) value, is the value at a given point. The value inside the parenthesis is your x value at a given point.  E.g. if you know that f(x) = 50x – 25, then you know that for whatever x-value you use, the corresponding y value will be that number times 50, minus 25.  Similarly, if you know that f(5) = 225, then you know that for the function f(x), the y value when x = 5 is 225.

Example 1:

“The number of cookies that Betty bakes for a party with t attendees is given by the function f(t) = 5t – 7.  How many cookies will Betty make for a party with 30 attendees?”  or “The number of cookies that Betty bakes for a party with t attendees is given by the function f(t) = 5t – 7.  If she bakes 43 cookies for a party, how many people are at that party?”

To solve these, figure out what you’re given and what you’re looking for, in terms of the function – i.e., do you have an f(x) value and you’re looking for an x value or vice versa. Then plug your given values into the equation to solve whatever you’re looking for.

The number of cookies that Betty bakes for a party with t attendees is given by the function f(t) = 5t – 7.  How many cookies will Betty make for a party with 30 attendees?

Here t, the number of attendees, is my x value, and f(t), the corresponding number of cookies, is my y value.  I’m given a number of attendees – 30 – and am trying to figure out the corresponding number of cookies. So, here goes the plugging-in process…

f(t) = 5t – 7
f(30) = 5(30) – 7  -> I’m plugging 30 in for t here, because I’m figuring out the value of f(t) when t = 30.
f(30) = 150 – 7 = 143.

Betty will make 143 cookies for a party with 30 attendees.

Example 2:

The number of cookies that Betty bakes for a party with t attendees is given by the function f(t) = 5t – 7.  If she bakes 43 cookies for a party, how many people are at that party?

Again, here the number of cookies, f(t), is my y-value and the number of attendees, t, is my x value. Here, I’m given a number of cookies – 43 – and am trying to figure out the corresponding number of people.  So, let’s plug in, shall we?

f(t) = 5t – 7
43 = 5t – 7  -> I’m plugging 43 in for f(t) there because I’m trying to figure out the value of t when f(t) = 43.
50 = 5t
10 = t.

There are 10 people at this 43-cookie party.

Tune in next time for some slightly trickier variations on this type of problem, and some other function tips. Until then, go forth and practice functions, and feel empowered in your function knowledge!

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Alice Rothman-Hicks is a Veritas Prep SAT 2400 instructor. Since graduating from Columbia University (Magna Cum Laude, Phi Beta Kappa), Alice has been teaching and tutoring test prep, helping students achieve their own academic successes. She scored a 2350 on the SAT.

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