Functions

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

Remember to read carefully! This problem includes a graph, which makes it doubly important to look closely and be cautious. Graphs can contain huge amounts of information, so read the question carefully to make sure you know what to look for. The function f is graphed in the xy-plane above. If the function g is defined by  , for how many values of x between -5 and 15 does g(x) equal 0?

First, read the question carefully. "for how many values of x between -5 and 15 does g(x) equal 0?" is long and complicated. Paraphrase it to pick out the most important parts. You are looking for how many times g(x)=0 when . Unfortunately, g(x) is defined only in terms of f(x), making it impossible to solve. Is the problem hopeless?

Not at all! The test makers provided a graph of y=f(x), so you can translate (slide) that upward 4 units to get the graph of y=f(x)+4 or y=g(x). Next, consider what will happen to the graph when g(x)=0. Since the graph we're discussing is y=g(x), look for the point where y=0. There are three on the graph. Now loop back to make sure you answered the question correctly.

The bottom line only asked about points where x is between -5 and 15. One of our three points is to the left of -5, so eliminate it and two are left. Now look at the answer choices:

A) None

B) One

C) Two

D) Three

E) More than three

E is the correct answer.

On sat.collegeboard.org, 45% of responses to this question were correct.

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