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Algebra 2 · Chapter 6 · Lesson 6.4 · Printable PDF

Composing Functions Algebraically Worksheet with Answer Key

5 problems on composing functions algebraically: simplifying compositions, writing a function as a composition of two or three, finding a student's error, and a road trip where distance feeds a fuel formula. 2 pages, with a worked answer key.

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Printable Composing functions algebraically worksheet with answer key - Algebra 2 (Page 1 PDF preview)
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What's on the worksheet

  1. Find and simplify each composition of the three functions:
    p(q(x))q(p(x))(q \circ r)(x)(r \circ q)(x)p(p(p(x)))
  2. Write each function as a composition of two or three given functions and check.
    2x + 64x^2 + 32x^2 + 12x + 184x^2 + 12x + 9
  3. Write each function as a composition of three simpler functions.
    \sqrt{(x - 1)^2 + 4}(2x - 5)^4 + 1\dfrac{5}{x^2 + 1} + 3\lvert x^3 - 8 \rvert
  4. Find the mistake in Aisha's work on a composition.
  5. Word problem: fuel left in a car after driving for some hours.

Teach it first

The free lesson teaches it with worked examples and practice problems.

Composing functions algebraically: the lesson ›

More Chapter 6 worksheets: Combined, composite and inverse functions