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Grade 11 · Math · Algebra 2

11th grade Combine functions: add, subtract, multiply, divide and compose worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Combine functions: add, subtract, multiply, divide and compose

Grade 11 Math Worksheet - Building Confidence

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  1. Read this first

    Table of f (x | f(x))

    -2 | 9; -1 | 6; 0 | 3; 1 | 0; 2 | -3. Table of g (x | g(x)): -2 | -7; -1 | -5; 0 | -3; 1 | -1; 2 | 1.

  2. Ari's worksheet has a table for f and a table for g. Combining works on the output columns, row by row. What is (f − g)(-1)?

  3. Table of f (x | f(x))

    0 | 5; 1 | 7; 2 | 9; 3 | 11; 4 | 13. Table of g (x | g(x)): 0 | 6; 1 | 3; 2 | 0; 3 | -3; 4 | -6.

  4. In a notebook, Bo copies the tables of f and g shown. The new function works row by row on the outputs. What is (f·g)(3)?

  5. Table of f (x | f(x))

    -1 | 4; 0 | 1; 1 | 0; 2 | 1; 3 | 4. Table of g (x | g(x)): -1 | -6; 0 | -1; 1 | 4; 2 | 9; 3 | 14.

  6. Esme fills a new column in pencil beside the tables of f and g. Each row combines the two outputs. What is (f − g)(2)?

  7. Table of f (x | f(x))

    -3 | -8; -2 | -5; -1 | -2; 0 | 1; 1 | 4. Table of g (x | g(x)): -3 | 10; -2 | 5; -1 | 2; 0 | 1; 1 | 2.

  8. On a puzzle card, Jun sees the tables of f and g. The outputs in each row are combined. What is (f·g)(1)?

  9. Table of f (x | f(x))

    -2 | 1; -1 | -2; 0 | 2; 1 | 0; 2 | -1. Table of g (x | g(x)): -2 | 0; -1 | 2; 0 | -1; 1 | -2; 2 | 1.

  10. Milo marks g(-1) = 2 in pencil on the g table. What is f(g(-1))?

  11. Table of f (x | f(x))

    0 | 3; 1 | 0; 2 | 4; 3 | 1; 4 | 2. Table of g (x | g(x)): 0 | 2; 1 | 4; 2 | 3; 3 | 0; 4 | 1.

  12. On a puzzle card, Noah reads g(0) = 2 from the g table. What is f(g(0))?

  13. On a worksheet, f(x) = x + 4 and g(x) = 2x − 6, so (f/g)(x) = (x + 4)/(2x − 6). Pia needs the x left out of the domain. What is it?

  14. In a notebook, Ren writes (f/g)(x) = (x + 7)/(3x + 12). One x-value is not in its domain. What is it?

  15. Tala divides f(x) = 3x − 1 by g(x) = 4x + 20 in pencil: (f/g)(x) = (3x − 1)/(4x + 20). Which x is left out of the domain?

  16. On a puzzle card, (f/g)(x) = (x + 9)/(6x − 3). Zee needs the one x-value with no output. What is it?

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11th grade Combine functions: add, subtract, multiply, divide and compose worksheet – printable
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About this worksheet

Combine functions: add, subtract, multiply, divide and compose. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can combine two functions row by row: f + g, f − g, f·g and f/g.
  • I can say which x-values are left out of the domain of f/g.
  • I can work out f(g(2)) from tables, rules or a graph, and write the rule for f(g(x)).

Standard: F-BF.A.1b, F-BF.A.1c (+)

Words to know

(f − g)(x): The output of f minus the output of g, for the same x.

(f·g)(x): The output of f times the output of g, for the same x.

domain: All the inputs a function can take.

composition f(g(x)): Put x into g, then put g's output into f.

inside / outside: In f(g(x)), g is inside and works first; f is outside.

Common mistakes

Your child subtracted f from g instead of g from f.

Your child added the two functions when the question asked for their product.

Your child did the two functions in the wrong order, g(f(x)) instead of f(g(x)).

What to say

Ask: in f − g, which function's output comes first?

Ask: what does the dot in f·g mean?

Ask: which function sits inside the brackets, so it goes first?

Questions parents ask

What is the most common mistake with combine functions: add, subtract, multiply, divide and compose?

Your child subtracted f from g instead of g from f.

How can I help my child with combine functions: add, subtract, multiply, divide and compose?

Ask: in f − g, which function's output comes first?

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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