Students distinguish relations from functions using mappings, tables, equations, graphs, and the vertical line test, and evaluate standard algebraic functions using function notation while respecting domain restrictions. They determine domains from equations, ranges from graphs, zeros, positive and negative intervals, and increasing, decreasing, or constant intervals, accounting for endpoints, holes, turning points, zeros, and undefined inputs. They interpret domain, range, intercepts, extrema, symmetry, discontinuities, end behavior, and other key graph features in mathematical and real-world contexts, including appropriate units and restrictions such as nonnegative time or whole-number quantities.
On this page:
- Master skills like “Determine zeros of a function”, “Distinguish relations from functions”, and “Evaluate functions using function notation” with unlimited, free practice problems
- Download (or modify) free worksheets on Functions and Function Notation you can use at home or in class with practice problems across all skills in this group including “Determine the range of a function from a graph”, “Determine the domain of a function from an equation”, “Interpret key features of a function from its graph”.
- Start working on adaptive units like “Functions - Domain and Range - Intro” or “Functions - Domain and Range - Practice” that include these skills and will introduce and scaffold the skills carefully for maximum learning.
Functions and Function Notation: Individual Skills
Master 8 individual skills with free practice problems. Mouseover to see the skill's practice problems. Create a free account to track your progress.
Your results
- Determine intervals where a function is increasing or decreasing
- Determine intervals where a function is positive or negative
- Determine the domain of a function from an equation
- Determine the range of a function from a graph
- Determine zeros of a function
- Distinguish relations from functions
- Evaluate functions using function notation
- Interpret key features of a function from its graph
Practice 'Determine intervals where a function is increasing or decreasing'
Select any skill in this group by hovering over the list above. Unlimited free practice problems, automatically graded.
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Download/Modify Free Grade 11 'Functions and Function Notation' Worksheet
Print this free 'Functions and Function Notation' worksheet to practice these skills away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.
This Worksheet Includes:
- Determine intervals where a function is increasing or decreasing
- Determine intervals where a function is positive or negative
- Determine the domain of a function from an equation
- Determine the range of a function from a graph
- Determine zeros of a function
- Distinguish relations from functions
- Evaluate functions using function notation
- Interpret key features of a function from its graph
Units Teaching These Skills
These adaptive units introduce, teach, or reinforce skills in this group (Functions and Function Notation) through scaffolded problems that grow in difficulty as concepts are understood.