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 - Challenge Me

NameDate

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

On a worksheet, f(x) = 3x − 2 and g(x) = x² + 4. Esme writes one rule for f(g(x)). Type powers like x^2. What is it?
In a notebook, Jun has f(x) = 2x + 1 and g(x) = x² − 3. What is g(f(x)), with like terms combined?
On a puzzle card, f(x) = x − 4 and g(x) = 2x² + 1. Luz needs g(f(x)) with like terms combined. What is it?
Milo's worksheet shows the graph of f and the rule g(x) = x − 3. At one x, f(g(x)) = 6. What is that x?
In a notebook, Noah has the graph of f and g(x) = x + 3. For which x is f(g(x)) = -4?
On a puzzle card, Ren sees the graph of f and the rule g(x) = x − 4. For which x is f(g(x)) = 7?
7.
On a worksheet, f(x) = x + 4 and g(x) = x² − x − 6. Tala writes the domain of (f/g)(x). What is it?
- All real numbers except -3 and 2
- All real numbers except -2 and 3
- All real numbers except -4
- All real numbers
8.
In a notebook, Zee has f(x) = x + 1 and g(x) = x² − 16. What is the domain of f/g?
- All real numbers
- All real numbers except 16, with no root taken
- All real numbers except -1
- All real numbers except -4 and 4
9.
Ari works in pencil: f(x) = x + 5 and g(x) = x² + 2x − 8. What is the domain of (f/g)(x)?
- All real numbers
- All real numbers except -2 and 4
- All real numbers except -4 and 2
- All real numbers except -5
10.
On a puzzle card, f(x) = x + 7 and g(x) = x² − 25. Bo needs the domain of f/g. What is it?
- All real numbers except -5 and 5
- All real numbers
- All real numbers except 25
- All real numbers except -7

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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