Functions
Practice evaluating and composing functions using function notation.
28 questions
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The graph of y = f(x) is shown, where the function f is defined by f(x) = ax 3 + bx 2 + cx + d and a, b, c, and d are constants. For how many values of x does f(x) = 0?
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The function f is defined by f(x) = 7x 3 . In the xy-plane, the graph of y = g(x) is the result of shifting the graph of y = f(x) down 2 units. Which equation defines function g?
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The function p is defined by p(n) = 7n 3 . What is the value of n when p(n) is equal to 56?
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Which of the following functions has(have) a minimum value at −3 ? I. f(x) = −6(3) x − 3 II. g(x) = −3(6) x
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The function f is defined by f(x) = ax 2 + bx + c, where a, b, and c are constants. The graph of y = f(x) in the xy-plane passes through the points (7, 0) and (−3, 0). If a is an integer greater than 1, which of the following could be the value of a + b ?
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A competitive diver dives from a platform into the water. The graph shown gives the height above the water y, in meters, of the diver x seconds after diving from the platform. What is the best interpretation of the x-intercept of the graph?
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The kinetic energy, in joules, of an object with mass 9 kilograms traveling at a speed of v meters per second is given by the function K, where K(v) = 9 ⁄ 2 v 2 . Which of the following is the best interpretation of K(34) = 5,202 in this context?
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Each term in the sequence below is two less than three times the previous term. What is the next term of the sequence?
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Each term in the sequence below is nine more than 1 ⁄ 3 the previous term. What is the value of y – x?
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Each term in the sequence below is 20 less than five times the previous term. What is the value of x + y?
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Each term in the sequence below is two less than 1 ⁄ 2 the previous term. What term of the sequence will be the first term to be a negative number?
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Each term in the sequence below is 16 more than –4 times the previous term. What is the value of x + y?
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All of the following are equal to the value of d EXCEPT
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If f(x) = 2x – 1 and g(x) = x 2 , what is the value of f(g(–3))?
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If f(x) = 3x + 2 and g(x) = 2x – 3, what is the value of g(f(–2))?
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If f(x) = 2x + 1 and g(x) = x – 2, what is the value of f(g(f(3)))?
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If f(x) = 6x + 4 and g(x) = x 2 – 1, what is the value of g(f(x))?
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If f(x) = 4 – 2x 2 and g(x) = 2√x, what is the value of f(g(x))?
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If w@z is equivalent to 3w – z, what is the value of (w@z)@z?
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If p&q is equivalent to p ⁄ q + pq, what is the value of q&p when p = 4 and q = –2?
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If j%k is equivalent to k j , what is the value of k%(j%k)?
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If a?b is equivalent to b – a ⁄ a + b , what is the value of a?(a?b) when a = 6 and b = –5?
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If x^y is equivalent to y 2 – x, what is the value of y^(y^y)?
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What is the domain of the function f(x) = 1 ⁄ x 2 – 9 ?
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What is the range of the function f(x) = x 2 – 4?
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Which of the following is true of f(x) = – x 2 ⁄ 2 ?
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Which of the following is true of f(x) = √(4x – 1)?
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Which of the following is true of f(x) = – 1 ⁄ √(x – 5) ?
Hard