Exercises: Combine Standard Function Types Using Arithmetic Operations

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Grade 9·21 problems·~28 min·Common Core Math - HS Functions·standard·hsf-bf-a-1b

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Warm-Up: Review What You Know

If $f(x) = x^2$ and $g(x) = 3x$ , what is $(f + g)(2)$ ?

If $f(5) = 12$ and $g(5) = 3$ , what is $(f - g)(5)$ ?

If $f(x) = 2x + 1$ and $g(x) = x^2$ , what is $(f \cdot g)(3)$ ?

Let $f(x) = 2x + 1$ and $g(x) = x^2$ . Which expression equals $(f + g)(x)$ ?

$x^2 + 2x + 1$

$2x^2 + 1$

$(2x + 1)(x^2)$

$2x^2 + 1$ (from substituting $g$ into $f$ )

Let $f(x) = 3x - 2$ and $g(x) = x + 5$ . Simplify $(f - g)(x) = ax + b$ . What is the coefficient $a$ ?

Let $f(x) = x + 4$ and $g(x) = x - 1$ . What is the constant term of $(f \cdot g)(x)$ ?

Let $f(x) = \sqrt{x}$ (domain: $x \geq 0$ ) and $g(x) = x + 3$ (domain: all reals). What is the domain of $(f + g)(x)$ ?

All real numbers

$x \geq 0$

$x \geq -3$

All reals except $x = 0$

Let $f(x) = x^2 + 1$ and $g(x) = x - 2$ , both with domain: all reals. What additional restriction applies to the domain of $(f/g)(x)$ ?

$x \neq -1$

$x \neq 0$

$x \neq 2$

No additional restriction

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