SAT Math: Functions Practice Questions
Test yourself on Functions with 10 original SAT practice questions. Pick an answer to see instant feedback and a full explanation.
Free original practice questions for study purposes. Open Exam Prep is an independent study resource and is not affiliated with, endorsed by, or sponsored by the makers of SAT.
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Answer the questions below — you get instant feedback and a full explanation for each.
1. If f(x) = 3x - 7, what is the value of f(5)?
Explanation. Substitute x = 5: f(5) = 3(5) - 7 = 15 - 7 = 8.
2. The function g is defined by g(x) = x² + 2x. What is g(-3)?
Explanation. g(-3) = (-3)² + 2(-3) = 9 - 6 = 3.
3. If h(x) = 2x + 1 and h(a) = 11, what is the value of a?
Explanation. Set 2a + 1 = 11, so 2a = 10 and a = 5.
4. For f(x) = 4 - x², for which value of x does f(x) reach its maximum?
Explanation. f(x) = 4 - x² is largest when x² is smallest, which is at x = 0, giving f(0) = 4. Any nonzero x decreases the value.
5. If f(x) = x² and g(x) = x + 3, what is f(g(2))?
Explanation. First g(2) = 2 + 3 = 5. Then f(5) = 5² = 25.
6. A function is defined by f(x) = (x - 4)(x + 2). What are the x-values where f(x) = 0?
Explanation. Set each factor to zero: x - 4 = 0 gives x = 4; x + 2 = 0 gives x = -2.
7. The table shows values of a linear function f: f(1)=5, f(3)=11, f(5)=17. What is f(0)?
Explanation. The slope is (11 - 5)/(3 - 1) = 3. So f(x) = 3x + b. Using f(1) = 5: 3(1) + b = 5, so b = 2. Then f(0) = 2.
8. If f(x) = 2^x, what is f(x+1) in terms of f(x)?
Explanation. f(x+1) = 2^(x+1) = 2·2^x = 2·f(x). The function doubles with each unit increase in x.
9. The function f is defined by f(x) = a(x - 2)² + 3. If the graph passes through (4, 11), what is the value of a?
Explanation. Substitute (4, 11): 11 = a(4 - 2)² + 3 = a(4) + 3. So 4a = 8 and a = 2.
10. If f(x) = x² - 6x + 5, the minimum value of f occurs at which x, and what is that minimum?
Explanation. Vertex x = -b/(2a) = 6/2 = 3. Then f(3) = 9 - 18 + 5 = -4. The parabola opens upward, so this is the minimum.
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FAQ
What does function notation like f(x) mean on the SAT?
f(x) is a rule that takes an input x and produces an output. To evaluate f(a), substitute a everywhere x appears. The notation does NOT mean f times x.
How do I handle composite functions like f(g(x))?
Work from the inside out. First compute g(x), then plug that result into f. For example, to find f(g(2)), find g(2) first, then apply f to that number.
How do I find the vertex of a quadratic function?
For f(x) = ax² + bx + c, the vertex x-coordinate is x = -b/(2a). Plug that back in to get the y-value. If written as a(x-h)² + k, the vertex is simply (h, k).