Determine the real domain and range of functions, zeros and - and -intercepts, intervals of positivity and negativity, vertical and horizontal asymptotes, and end behavior for common polynomial, rational, exponential, and logarithmic functions. Interpret graphs, tables, formulas, and first-derivative information to identify intervals of increase and decrease, local and absolute extrema, intervals of concavity, and points of inflection over the stated domain. Sketch coherent function graphs by integrating these characteristics, including symmetry, discontinuities, periodicity where applicable, and qualitative behavior while distinguishing exact features from approximations.
On this page:
- Master skills like “Identify local and absolute extrema”, “Determine end behaviour of a function”, and “Identify vertical and horizontal asymptotes” with unlimited, free practice problems
- Download (or modify) free worksheets on Function Characteristics you can use at home or in class with practice problems across all skills in this group including “Identify zeros and intercepts of a function”, “Determine the domain and range of a function”, “Determine intervals of concavity from a graph”.
- Start working on adaptive units like “Derivatives and Critical Points - Intro” or “Functions - End Behaviour - Intro” that include these skills and will introduce and scaffold the skills carefully for maximum learning.
Function Characteristics: 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 end behaviour of a function
- Determine intervals of concavity from a graph
- Determine intervals where a function is increasing or decreasing
- Determine intervals where a function is positive or negative
- Determine the domain and range of a function
- Identify local and absolute extrema
- Identify vertical and horizontal asymptotes
- Identify zeros and intercepts of a function
Practice 'Determine end behaviour of a function'
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 12 'Function Characteristics' Worksheet
Print this free 'Function Characteristics' worksheet to practice these skills away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.
This Worksheet Includes:
- Determine end behaviour of a function
- Determine intervals of concavity from a graph
- Determine intervals where a function is increasing or decreasing
- Determine intervals where a function is positive or negative
- Determine the domain and range of a function
- Identify local and absolute extrema
- Identify vertical and horizontal asymptotes
- Identify zeros and intercepts of a function
Units Teaching These Skills
These adaptive units introduce, teach, or reinforce skills in this group (Function Characteristics) through scaffolded problems that grow in difficulty as concepts are understood.