1.1: Function Notation, Domain, and Range | Algebra 2 Honors

How it works

A function assigns exactly one output to each permitted input. Evaluate by replacing every occurrence of the variable. A real-valued square root requires a nonnegative radicand, and a denominator cannot be zero. Range describes actual outputs and may be narrower than all real numbers.

f(a)\text{ means substitute }a\text{ for the input.}

Worked examples

Example 1

For $\displaystyle f(x)=x^2-3x$ , find $\displaystyle f(-2)$ .

$\displaystyle f(-2)=(-2)^2-3(-2)=4+6=10$ .

Example 2

Find the domain of $\displaystyle g(x)=\sqrt{x-4}$ .

The radicand must satisfy $\displaystyle x-4\ge0$ , so the domain is $\displaystyle [4,\infty)$ .

Problems

Problem 1.1.1

Find the domain of $\displaystyle f(x)=1/(x+3)$ .

Show worked solution

The denominator cannot be zero, so $\displaystyle x\ne-3$ . The domain is all real numbers except $\displaystyle -3$ .

Problem 1.1.2

Find the domain of $\displaystyle g(x)=\sqrt{7-2x}$ .

Show worked solution

$\displaystyle 7-2x\ge0$ , giving $\displaystyle x\le7/2$ . The domain is $\displaystyle (-\infty,7/2]$ .

Problem 1.1.3

Use the graph of $\displaystyle f(x)=(x-2)^2+1$ to give its domain and range.

The upward parabola y = (x − 2) squared + 1 has its minimum at height 1. — Compare allowed inputs with actual outputs.

Show worked solution

Every real input is allowed, so the domain is $\displaystyle \mathbb{R}$ . The minimum output is $\displaystyle 1$ , so the range is $\displaystyle [1,\infty)$ .

The upward parabola y = (x − 2) squared + 1 has its minimum at height 1. Domain: all real numbers; range: y ≥ 1. — Domain: all real numbers; range: y ≥ 1.

Lesson Problems PDF Solutions PDF Unit MCQ

How it works

Worked examples

Example 1

Example 2

Problems

Problem 1.1.1

Problem 1.1.2

Problem 1.1.3

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