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Graphs of Functions
Plotting input-output pairs on a coordinate plane shows the shape of a function.
Plotting a Function
Every input-output pair (, f()) can be plotted as a point on a coordinate plane, with along the horizontal axis and f() along the vertical axis. Joining the points shows the shape of the function.
A function of the form f() = mx + c always graphs as a straight line. A function with an term, like f() = , graphs as a curve called a parabola.
Coordinate plane
Change a value and watch: f() = is a straight line. controls how steep it is; c is where it crosses the vertical axis.
Coordinate plane
Change a value and watch: f() = is a curve, not a straight line. Try changing a, b, and c.
Example 1 — plotting points
Plot f() = for , , , , .
- f, f, f() = , f() = , f() =
- The points are (, ), (, ), (, ), (, ), (, )
- Joining them makes a straight line, sloping upward from left to right.
Practice
Which function will graph as a straight line?
More lessons in Sets and Functions · Next: Course Exam · Previous: Inverse Functions
