# Functions

Is there always another explanation or point of view?  Before you answer this released SAT essay prompt, check out this article that is part current event and part historical example with a literary connection thrown in just for fun.  Richard the III was a real king who is best known as a villain in Shakespeare’s work.  Read about what happened to him and why he is appearing in the news now.  There are far too many themes in this article to name them all, so come up with about a dozen ways you could connect this example to an essay prompt.  Then memorize a few of the most interesting facts so that you can use them to support your opinion on any of the themes that show up in your SAT essay prompt.

Note: The identity of King Richard the III has been confirmed.  Read here for details.

## Algebra: Functions

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

Always read the problem carefully, identify the bottom line, and assess your options for solving the problem before you attack the problem.  When you have an answer, loop back to verify that it matches the bottom line.

The function y = f(x), defined for -1.5 ≤ x ≤ 1.5, is graphed above. For how many different values of is f(x) = 0.2?

Bottom Line: # times f(x) = .2

Assess your Options:  Some students will skip this problem, thinking that it requires a lot of time to somehow write a formula for the function from the graph.  However, once you know what you are looking at, this is one of the easiest and fastest problems on the test!  All that you have to do is read the graph!

Attack the Problem:  You know that f(x) = .2 is the same thing as y = .2.  Anytime you see f(x), you can just substitute a y for f(x) if that clarifies the problem in your head.  If y is constant, you know that it will be a horizontal line at .2.  Draw that line on your graph.

Anywhere that the line crosses the function f(x), that function is equal to .2.  Count up the number of intersections between the line that you drew and the original function.  There are four.  That means that f(x) = .2 four times.