Evaluate quadratic and exponential functions, and model real-world growth and decay scenarios.
64 original nonlinear functions questions in the SAT Ranker bank, with instant scoring and an Elo-based rank once you sign up. Below are a few free samples with full explanations.
If f(x) = 2x² − 3, what is f(−2)?
f(−2) = 2(−2)² − 3 = 2(4) − 3 = 8 − 3 = 5.
If f(x) = -2x² + 5, what is f(5)?
f(5) = -2(5)² + 5 = -2(25) + 5. The answer is -45. -5 multiplies by 5 instead of squaring it; 55 treats (5)² as -25, losing the sign of the square; -55 squares correctly but subtracts the 5 instead of adding it.
If f(x) = x² + 9, what is f(-3)?
f(-3) = 1(-3)² + 9 = 1(9) + 9. The answer is 18. 6 multiplies by -3 instead of squaring it; 0 treats (-3)² as -9, losing the sign of the square.
If f(x) = x² + 2, what is f(6)?
f(6) = 1(6)² + 2 = 1(36) + 2. The answer is 38. 8 multiplies by 6 instead of squaring it; -34 treats (6)² as -36, losing the sign of the square; 34 squares correctly but subtracts the 2 instead of adding it.
If f(x) = -2x² + 2, what is f(-1)?
f(-1) = -2(-1)² + 2 = -2(1) + 2. The answer is 0. 4 multiplies by -1 instead of squaring it; -4 squares correctly but subtracts the 2 instead of adding it.