Functions, Domain, and Range

Explore function rule, domain restrictions, range and graph reading.

Lesson 2 of 43 parts Practice Flashcards

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Function Rule

Objective: Explain function rule and use it to solve or interpret a problem.

A function assigns exactly one output to every allowed input. Different inputs can share one output without violating the rule. Yes; the restriction is on multiple outputs for one input.

Worked examples

Try itFunctions, Domain, and Range — practice 1.1: For f(x)=2x+6, find f(5).Show answer

Step 1: Replace x with 5: f(5)=2(5)+6. Step 2: Multiply: 10+6. Step 3: Add: 16.

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Function Rule

Objective: Explain function rule and use it to solve or interpret a problem.

A function assigns exactly one output to every allowed input. Different inputs can share one output without violating the rule. Yes; the restriction is on multiple outputs for one input.

Worked examples

Try itFunctions, Domain, and Range — practice 1.1: For f(x)=2x+6, find f(5).Show answer

Step 1: Replace x with 5: f(5)=2(5)+6. Step 2: Multiply: 10+6. Step 3: Add: 16.

Domain Restrictions

Objective: Explain domain restrictions and use it to solve or interpret a problem.

The domain includes only inputs for which a rule is defined and which make sense in context. A denominator cannot be zero and an even root needs a nonnegative radicand over the reals. Making the original denominator zero.

Worked examples

Try itFunctions, Domain, and Range — practice 2.1: For f(x)=1/(x−8), which x-value is excluded?Show answer

Step 1: The denominator cannot be zero. Step 2: Solve x−8=0. Step 3: Therefore x=8 is excluded.

Range and Graph Reading

Objective: Explain range and graph reading and use it to solve or interpret a problem.

The range consists of outputs actually produced by inputs from the stated domain. A parabola opening upward has a least output at its vertex over the real domain. Changing allowed inputs can change available outputs.

Worked examples

Try itFunctions, Domain, and Range — practice 3.1: For y=(x−11)²+3, find the minimum output.Show answer

Step 1: A square is at least zero. Step 2: At x=11, the square is zero. Step 3: The minimum output is 3.

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