Composite Functions Challenge

Froggy Jumps

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Test your composite skills

Created by

Jesus Andres Jaimes Leon

Colombia

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Froggy Jumps Composite Functions ChallengeOnline version Test your composite skills by Jesus Andres Jaimes Leon 1 What is the definition of a composite function f ∘ g a Apply f first, then apply g to the result b Take the average of f and g outputs c Apply g first, then apply f to the result 2 If f(x)=2x+3 and g(x)=x−1, what is (f∘g)(2)? a (f(g(2))) = f(1) = 5 b (f(g(2))) = f(0) = 3 c (f∘g)(2) = 2*(2−1)+3 = 5 3 True or False: (f∘g)(x) is defined for all x where g(x) is in the domain of f a False b Only when f is linear c True 4 Given f(x)=x^2 and g(x)=√x, what is (f∘g)(4)? a (f∘g)(4) = f(√4) = f(2) = 4 b (f∘g)(4) = 8 c (f∘g)(4) = 2 5 If f(x)=3x and g(x)=x+5, what is (g∘f)(-1)? a g(f(-1)) = -4 b g(f(-1)) = g(-3) = 2 c g∘f(-1) is undefined 6 Which property relates to (f∘g)(x) when f is constant? a (f∘g)(x) grows quadratically b (f∘g)(x) is a constant function c (f∘g)(x) is increasing 7 If f(x)=√x and g(x)=x+4, what is (f∘g)(9)? a (f∘g)(9) = √9 + 4 b (f∘g)(9) = 9 + 4 c (f∘g)(9) = √(13) 8 Which is a correct domain consideration for (f∘g)? a Domain is always all real numbers b Need x-values such that g(x) lies in the domain of f c Only the domain of g matters 9 If f is defined on all real numbers and g is defined for x≥0, what is the domain of (f∘g) if g(x)=−x? a Domain where x≤0 b All real numbers c Domain where x≥0 10 Which is an example of simplifying (f∘g)(x) correctly? a Multiply f(x) and g(x) together b Compute f(x) first, then apply g c Compute g(x) first, then apply f to the result

Froggy Jumps

Composite Functions ChallengeOnline version

Test your composite skills

by Jesus Andres Jaimes Leon

What is the definition of a composite function f ∘ g

Apply f first, then apply g to the result

Take the average of f and g outputs

Apply g first, then apply f to the result

If f(x)=2x+3 and g(x)=x−1, what is (f∘g)(2)?

(f(g(2))) = f(1) = 5

(f(g(2))) = f(0) = 3

(f∘g)(2) = 2*(2−1)+3 = 5

True or False: (f∘g)(x) is defined for all x where g(x) is in the domain of f

False

Only when f is linear

True

Given f(x)=x^2 and g(x)=√x, what is (f∘g)(4)?

(f∘g)(4) = f(√4) = f(2) = 4

(f∘g)(4) = 8

(f∘g)(4) = 2

If f(x)=3x and g(x)=x+5, what is (g∘f)(-1)?

g(f(-1)) = -4

g(f(-1)) = g(-3) = 2

g∘f(-1) is undefined

Which property relates to (f∘g)(x) when f is constant?

(f∘g)(x) grows quadratically

(f∘g)(x) is a constant function

(f∘g)(x) is increasing

If f(x)=√x and g(x)=x+4, what is (f∘g)(9)?

(f∘g)(9) = √9 + 4

(f∘g)(9) = 9 + 4

(f∘g)(9) = √(13)

Which is a correct domain consideration for (f∘g)?

Domain is always all real numbers

Need x-values such that g(x) lies in the domain of f

Only the domain of g matters

If f is defined on all real numbers and g is defined for x≥0, what is the domain of (f∘g) if g(x)=−x?

Domain where x≤0

All real numbers

Domain where x≥0

Which is an example of simplifying (f∘g)(x) correctly?

Multiply f(x) and g(x) together

Compute f(x) first, then apply g

Compute g(x) first, then apply f to the result

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Composite Functions Challenge

Froggy Jumps

About this activity

Created by

Download the paper version to play

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Composite Functions ChallengeOnline version

by Jesus Andres Jaimes Leon

What is the definition of a composite function f ∘ g

If f(x)=2x+3 and g(x)=x−1, what is (f∘g)(2)?

True or False: (f∘g)(x) is defined for all x where g(x) is in the domain of f

Given f(x)=x^2 and g(x)=√x, what is (f∘g)(4)?

If f(x)=3x and g(x)=x+5, what is (g∘f)(-1)?

Which property relates to (f∘g)(x) when f is constant?

If f(x)=√x and g(x)=x+4, what is (f∘g)(9)?

Which is a correct domain consideration for (f∘g)?

If f is defined on all real numbers and g is defined for x≥0, what is the domain of (f∘g) if g(x)=−x?

Which is an example of simplifying (f∘g)(x) correctly?

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