Functions & graphs
Read graphs and reason through function composition, transformations, inverses and domains.
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Example
Example
Example · Standard
What is the maximum value of f?
The function accepts all real inputs. The graph shows f.
Connected rules · Composition and inverse composition, translations, piecewise rules and vertices
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6 questions · No time limit
- Questions answered
- 0 / 6
- Active time
- 0:00
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Read the function and its domain, then choose the requested value.
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Reload pageExplore the method
Connect inputs and outputs, combine graphs and compositions, and keep every restriction when finding a domain or inverse.
On by default unless you turn it off. Saved choices are kept. Shares starts, completions, replays and error categories. For ChatGPT visits, starts and completions may include the first QuickenBrain page and country. No answers, drawings or names.
How this data is usedHelp
Each round draws six different ideas from the selected level. Easy connects formulas, points, slopes and intercepts. Standard adds compositions, inverse compositions, translations, piecewise rules and quadratic vertices. Challenge combines restrictions with nested functions, disconnected domains and intersections of two graphs. Coordinates stated in the question are exact. Graph windows show only part of an unrestricted function. Use the printed scales, not the angle of a line. Each review explains the method, works the calculation and checks a common mistake. These are original practice questions, not an official examination or a validated assessment.
Each round has six questions and no time limit. Choosing an answer locks it. Review the steps, then move to the next question. Finish all six to save the round. Active time includes reviewing the steps, but does not count time when this page is hidden. Speed does not affect your score.
Use Tab and Enter or Space to choose an answer. The number keys also select answers, except when another control is focused. After an answer, Enter goes to the next question.
Original practice puzzles, not a standardized assessment.
About this practice
Follow the input through a function, connect the rule to its graph, and keep every domain restriction in view.
Learn a method
Read functions and graphsReport a problem
On by default unless you turn it off. Saved choices are kept. Shares starts, completions, replays and error categories. For ChatGPT visits, starts and completions may include the first QuickenBrain page and country. No answers, drawings or names.
How this data is used