Grade 11 · Math · Algebra 2

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

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

Grade 11 Math Worksheet

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Circle the best answer, or write your answer on the line.

On a worksheet, f(x) = 3x² − 2x + 1 and g(x) = x² + 4x − 5. Ari writes one rule for the new function. Type powers like x^2. What is (f − g)(x)?
In a notebook, Bo has f(x) = x + 3 and g(x) = 2x − 5. What is (f·g)(x), with like terms combined?
Esme combines f(x) = 4x² + x − 3 and g(x) = 2x² − 5x + 4 in pencil. Type powers like x^2. What is (f − g)(x)?
On a puzzle card, f(x) = 3x − 4 and g(x) = x + 6. Jun needs one rule with like terms combined. What is (f·g)(x)?
In a notebook, Luz has f(x) = 2x² − 5 and g(x) = 4x² + x + 3. What is (f + g)(x), with like terms combined?
On a worksheet, f(x) = x² − 5 and g(x) = 2x + 1. Milo works out f(g(-2)). What is it?
In a notebook, Noah has f(x) = 3x − 4 and g(x) = x² + 2. What is g(f(3))?
On a puzzle card, f(x) = x² − 2x and g(x) = 4x + 1. Ren needs g(f(-1)). What is it?
9.
Ari works in pencil: f(x) = x + 6 and g(x) = 2x − 7. What is the domain of (f/g)(x)?
- All real numbers
- All real numbers except -7/2
- All real numbers except 7/2
- All real numbers except -6
10.
On a puzzle card, f(x) = x + 8 and g(x) = 6x + 4. Bo needs the domain of f/g. What is it?
- All real numbers except 2/3
- All real numbers except -8
- All real numbers except -2/3
- All real numbers

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

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 (+)

(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.

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)).

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?

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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