Read a graph as a relationship between quantities. Check axes and scale, connect points to an equation, and interpret the change between two points.
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Functions & graphs
Connect a rule to its inputs, outputs, table, and graph. Read axes and scale carefully, use function notation, and explain what a point or change represents.
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Explore functions & graphs
Read f(x) as the output of a function at an input. Evaluate a rule carefully, check its domain, and connect notation to a table or graph.
What you’ll learn
- Read a graph using its axes, units, and scale.
- Evaluate a function at a specified input.
- Connect a rule, table, and graph as views of one relationship.
One relationship, several representations
A rule, a table, and a graph can describe the same input-output relationship. Each makes something easier to see: a rule supports calculation, a table shows selected values, and a graph reveals a pattern over a range.
A function assigns one output to each allowed input
Two inputs may produce the same output. The defining condition is that one permitted input cannot have two different outputs from the same function. The domain describes which inputs are allowed.
Read the display before drawing a conclusion
Check axis labels, units, intervals, and the displayed range. A line’s visual steepness can change when its axes are rescaled even though the underlying numerical rate remains the same.
Keep exploring
Graphs & coordinatesRead a graph as a relationship between quantities. Check axes and scale, connect points to an equation, and interpret the change between two points.Function notationRead f(x) as the output of a function at an input. Evaluate a rule carefully, check its domain, and connect notation to a table or graph.Quadratic equationsRecognize a quadratic equation and connect its roots to factors or a graph. Work through a factorable example and check every proposed solution.LimitsDistinguish a function’s value at a point from the value it approaches nearby. Work through a removable gap and explain why direct substitution can be misleading.
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