Lesson 5-6: Qualitative Graphs

Property

A qualitative graph represents the relationship between two quantities without using numerical values on the axes. It focuses on the general shape and behavior of the relationship rather than exact data points.

• Independent Variable (x-axis): The cause or the input (often Time) goes on the horizontal axis.
• Dependent Variable (y-axis): The effect or the output goes on the vertical axis.

Examples

• A graph with "Time" on the x-axis and "Speed" on the y-axis shows a line going upward. Even without numbers, this qualitative graph tells us that speed is increasing as time passes.
• A graph showing "Volume" on the x-axis and "Pressure" on the y-axis shows a downward curve. This indicates that as volume increases, pressure decreases.

Explanation

Qualitative graphs describe the general behavior of a relationship between two variables without relying on a numeric scale. Instead of plotting exact coordinates, you analyze the overall shape of the line or curve to quickly visualize trends. Always ask yourself: "Which one do I count first (x-axis), and which one happens as a result (y-axis)?"

Property

A function is increasing on an interval if as $x$ values move from left to right, the $y$ values rise (positive slope).
A function is decreasing on an interval if as $x$ values move from left to right, the $y$ values fall (negative slope).

Examples

Property

A function is constant on an interval if its output value ($y$-value) does not change as the input value ($x$-value) increases.
On a graph, this appears as a horizontal line segment.

Examples