Precalculus Combining and Composing Functions Test with Point Values (PDF)

Precalculus math test: Combining and Composing Functions – Maths PDF

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This function operations test for Precalculus covers combining and composing functions (Common Core F-BF.A.1b, F-BF.A.1c), with a free PDF to print.

This 20-point test covers operations on functions, composition, domains and a model problem (F-BF.A.1b, F-BF.A.1c). You have 45 minutes. Show your work.

Time and points

About this test

Grade: Precalculus
Chapter: Combining and Composing Functions
Standards: F-BF.A.1b, F-BF.A.1c
Time: 45 minutes
Total: 20 points

Function operations test: questions

Question 1 – Sum and product [2 pts]

Let $f(x)=x^{2}-2x$ and $g(x)=2x+5$. Find $(f+g)(3)$ and $(fg)(-1)$.

Question 2 – Composite formulas [2 pts]

Let $f(x)=x^{2}+1$ and $g(x)=3x-2$. Write $f(g(x))$ and $g(f(x))$ in standard form.

Question 3 – Table composition [2 pts]

Values of f and g.

Find $f(g(2))$ and $g(g(0))$.

Question 4 – Domain of a quotient [2 pts]

Let $f(x)=\sqrt{x+1}$ and $g(x)=x-5$. Find the domain of $\frac{f}{g}$.

Question 5 – Domain of a composite [3 pts]

Number line for graphing the domain.

Let $f(x)=\frac{1}{x-2}$ and $g(x)=\sqrt{x}$. Find the domain of $f(g(x))$ in interval notation.

Question 6 – Decompose [2 pts]

Write each function as $f(g(x))$: (a) $h(x)=\frac{1}{x^{2}+4}$; (b) $k(x)=|3x-7|$.

Question 7 – Evaluate composites [2 pts]

Let $f(x)=2x-1$ and $g(x)=x^{2}$. Find $(g\circ f)(3)$ and $(f\circ g)(3)$.

Question 8 – Bakery model [3 pts]

Hours to cookies to revenue.

Jamal’s stand bakes $n(h)=15h$ cookies in $h$ hours and sells them for $R(n)=0.75n$ dollars. (a) Write $R(n(h))$. (b) Find the revenue after $8$ hours. (c) Find the hours needed to reach $\$180$.

Question 9 – Inverse check [2 pts]

Show that $f(x)=3x-7$ and $g(x)=\frac{x+7}{3}$ satisfy $f(g(x))=x$ and $g(f(x))=x$.

Key facts behind this function operations test

Key facts

(f+g)(x) = f(x) + g(x); the same pattern holds for difference and product.
(f/g)(x) = f(x)/g(x) requires g(x) not equal to 0.
(f∘g)(x) = f(g(x)): work from the inside out.
In general f(g(x)) is not equal to g(f(x)).
Domain of f(g(x)): x must be in the domain of g, and g(x) in the domain of f.

How to use this function operations test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Precalculus chapters: Precalculus math.

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