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SAT Nonlinear functions practice questions
Quadratic and exponential functions: vertices, zeros, growth and decay, and transformations. Below are 20 free practice questions sorted from easy to hard. Open one to answer it and see the explanation.
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Question 1
The function f is defined by f(x) = x^2 - 3x + 2. What is the value of f(4)?EasyQuestion 2
A colony of bacteria has 500 bacteria at time t = 0, and the number of bacteria doubles every hour. Which function givesEasyQuestion 3
The function g is defined by g(x) = 2^x + 5. What is the value of g(3)?EasyQuestion 4
The function f is defined by f(x) = (x - 3)(x + 5). What are the x-intercepts of the graph of y = f(x) in the xy-plane?EasyQuestion 5
The value, in dollars, of a car t years after it was purchased is modeled by V(t) = 24,000(0.85)^t. Which statement bestEasyQuestion 6
The function h is defined by h(x) = 3x^2 - 7. What is the value of h(-2)?EasyQuestion 7
What is the vertex of the graph of y = 2(x + 3)^2 - 8 in the xy-plane?MediumQuestion 8
The function f is defined by f(x) = x^2 + bx + 12, where b is a constant. If f(2) = 0, what is the other value of x for MediumQuestion 9
The height, in feet, of a ball t seconds after it is thrown is modeled by h(t) = -16t^2 + 64t + 5. What is the maximum hMediumQuestion 10
The table shows three values of x and their corresponding values of f(x) for the exponential function f. Which equation MediumQuestion 11
For the exponential function f, f(0) = 5 and f(1) = 15. What is the value of f(3)?MediumQuestion 12
The function f is defined by f(x) = x^2 - 6x + 13. What is the minimum value of f(x)?MediumQuestion 13
The graph of a quadratic function in the xy-plane has x-intercepts at (-1, 0) and (5, 0) and a y-intercept at (0, -10). MediumQuestion 14
The function f is defined by f(x) = x^2. The function g is defined by g(x) = f(x - 2) + 3. What is the vertex of the graMediumQuestion 15
The function f is defined by f(x) = x^2 - 4x. The graph of y = g(x) is the result of reflecting the graph of y = f(x) acHardQuestion 16
The function m(t) = 80(12)^t6 gives the mass, in grams, of a radioactive sample t days after it was measured. Which funcHardQuestion 17
A quadratic function f has a minimum value of -6. The graph of y = f(x) in the xy-plane passes through the points (-1, 2HardQuestion 18
The function f is defined by f(x) = x^2 + 2x - 8. The function g is defined by g(x) = f(x + 3). What is the sum of the xHardQuestion 19
The number of users of an app t months after launch is modeled by N(t) = 2,400(1.2)^t3. According to the model, by what HardQuestion 20
The quadratic function f is defined by f(x) = ax^2 + bx + c, where a, b, and c are constants, a < 0, and c > 0. Which ofHard
The function f is defined by f(x) = x^2 - 3x + 2. What is the value of f(4)?EasyQuestion 2
A colony of bacteria has 500 bacteria at time t = 0, and the number of bacteria doubles every hour. Which function givesEasyQuestion 3
The function g is defined by g(x) = 2^x + 5. What is the value of g(3)?EasyQuestion 4
The function f is defined by f(x) = (x - 3)(x + 5). What are the x-intercepts of the graph of y = f(x) in the xy-plane?EasyQuestion 5
The value, in dollars, of a car t years after it was purchased is modeled by V(t) = 24,000(0.85)^t. Which statement bestEasyQuestion 6
The function h is defined by h(x) = 3x^2 - 7. What is the value of h(-2)?EasyQuestion 7
What is the vertex of the graph of y = 2(x + 3)^2 - 8 in the xy-plane?MediumQuestion 8
The function f is defined by f(x) = x^2 + bx + 12, where b is a constant. If f(2) = 0, what is the other value of x for MediumQuestion 9
The height, in feet, of a ball t seconds after it is thrown is modeled by h(t) = -16t^2 + 64t + 5. What is the maximum hMediumQuestion 10
The table shows three values of x and their corresponding values of f(x) for the exponential function f. Which equation MediumQuestion 11
For the exponential function f, f(0) = 5 and f(1) = 15. What is the value of f(3)?MediumQuestion 12
The function f is defined by f(x) = x^2 - 6x + 13. What is the minimum value of f(x)?MediumQuestion 13
The graph of a quadratic function in the xy-plane has x-intercepts at (-1, 0) and (5, 0) and a y-intercept at (0, -10). MediumQuestion 14
The function f is defined by f(x) = x^2. The function g is defined by g(x) = f(x - 2) + 3. What is the vertex of the graMediumQuestion 15
The function f is defined by f(x) = x^2 - 4x. The graph of y = g(x) is the result of reflecting the graph of y = f(x) acHardQuestion 16
The function m(t) = 80(12)^t6 gives the mass, in grams, of a radioactive sample t days after it was measured. Which funcHardQuestion 17
A quadratic function f has a minimum value of -6. The graph of y = f(x) in the xy-plane passes through the points (-1, 2HardQuestion 18
The function f is defined by f(x) = x^2 + 2x - 8. The function g is defined by g(x) = f(x + 3). What is the sum of the xHardQuestion 19
The number of users of an app t months after launch is modeled by N(t) = 2,400(1.2)^t3. According to the model, by what HardQuestion 20
The quadratic function f is defined by f(x) = ax^2 + bx + c, where a, b, and c are constants, a < 0, and c > 0. Which ofHard