Function Operations Answers

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If f(x) and g(x) are quadratic functions but (f + g)(x) produces the graph below, which statement must be true?

The leading coefficients of f(x) and g(x) are opposites.

The leading coefficients of f(x) and g(x) are opposite reciprocals.

The leading coefficients of f(x) and g(x) are the same.

The leading coefficients of f(x) and g(x) are reciprocals.

If f(x) = 4 – x2 and g(x) = 6x, which expression is equivalent to (g – f)(3)?

6 – 3 – (4 + 3)2

6 – 3 – (4 – 32)

6(3) – 4 + 32

6(3) – 4 – 32

If f(x) = x2 – 2x and g(x) = 6x + 4, for which value of x does (f + g)(x) = 0?

–4

–2

If f(x) = 3 – 2x and , what is the value of ?

–169

–1

104

If f(x) = 3x2 + 1 and g(x) = 1 – x, what is the value of (f – g)(2)?

If and , what is the value of (f – g)(144)?

–84

–60

Which expression is equivalent to (f + g)(4)?

f(4) + g(4)

f(x) + g(4)

f(4 + g(4))

4(f(x) + g(x))

If f(x) = 16x – 30 and g(x) = 14x – 6, for which value of x does (f – g)(x) = 0?

–18

–12

The graphs of f(x) and g(x) are shown below. Which of the following is the graph of (g – f)(x)?

On a coordinate plane, a straight line with a negative slope goes through points (negative 2, 6), (0, 0), and (2, negative 6)

On a coordinate plane, a straight line with a negative slope goes through points (negative 6, 6), (0, 0), and (6, negative 6).

On a coordinate plane, a straight line with a positive slope goes through points (negative 2, negative 6), (0, 0), and (2, 6).

On a coordinate plane, a straight line with a positive slope goes through points (negative 6, negative 6), (0, 0), and (6, 6).

If p(x) = x2 – 1 and , which expression is equivalent to (p – q)(x)?

5(x – 1) – x2 – 1

(5x – 1) – (x2 – 1)

(x2 – 1) – 5(x – 1)

(x2 – 1) – 5x – 1

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