SAT Math Multiple Choice Question 108: Answer and Explanation

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Question: 108


In the figure above, the graph of y = f(x) is shown. Which of the following could be the equation of f(x) ?

  • A. f(x) = - x + 3
  • B. f(x) = - x - 3
  • C. f(x) = x - 3
  • D. f(x) = x + 3

Correct Answer: D


D The graph of f(x) has a y-intercept at y = 3. Because of this, we know that when y = 3, x = 0. f(x) must then satisfy the condition that f(0) = 3. This is true only for (A) and (B). Alternatively, by recognizing that each equation is in the slope-intercept form: f(x) = y = mx + b, where b is the y-intercept, we can reach the same conclusion. Next, notice that the slope of the line is positive. That is, as the value of x increases, so too does y. Returning to the slope-intercept form, m gives the slope of the line. Only (D) has a positive coefficient (m). Choice (D), then, is the correct function.

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