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Different Features of a Graph

4.13.1 Different Features of a Graph

4.13.1 • Different Features of a Graph

Warm Up

Examine the following 4 graphs and think about why 1 of the graphs does not belong in the same group as the other 3.

A graph with a line in quadrant I that has a negative slope, intercepting the y-axis and x-axis. A step function graph with horizontal segments increasing from left to right. Each step starts with a closed black dot and ends with an open white dot, starting at the origin and extending rightward.
A graph with horizontal and vertical axes. The horizontal line starts at a y-intercept and extends right, representing a constant value. Both axes have arrows indicating positive directions. A graph showing a wave with increasing and then decreasing amplitude, centered along the horizontal axis. Both vertical and horizontal axes are drawn, with the origin marked.
This table presents various mathematical graph examples, including linear, step, and oscillating functions.

Which graph does not belong? Be prepared to show your reasoning.

Compare your answers:

Any answer could be correct.

Graph A doesn’t belong because:

  • It is the only graph that has a positive vertical intercept and a positive horizontal intercept.
  • It is the only one that has a constant, negative rate of change.

Graph B doesn’t belong because:

  • It is the only graph that is not a continuous curve and has multiple pieces.
  • It is the only one that shows both points and lines.

Graph C doesn’t belong because:

  • It is the only graph that has a constant y-value.

Graph D doesn’t belong because:

  • It is the only graph whose y-value increases and decreases multiple times.
  • It is the only graph that is not a simple line or curve and that has wave-like features.