​Characteristics of Graphs

​All graphs are different!

​So, we have a lot of ways to describe what they look like and mean.

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​This lesson will go over some of the vocab used to describe characteristics of graphs.

​y-intercept

The y-intercept is the place where the graph of the function crosses the y-axis.

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​The function to the right has a

y-intercept of -6.

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​Sometimes we use b as the variable for the y-intercept.

​x-intercept(s)

An x-intercept is any place at which the graph of a function crosses the x-axis. It is possible for functions to have more than one x-intercepts (or zero!).

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​The function to the right has three

x-intercepts at -3, -2, and 1.

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​X-intercepts can also be called roots, solutions, or zeroes.

​Positive/Negative Intervals

It can be interesting to tell when a function is positive (above the x-axis) vs. when it is negative (below the x-axis). Remember to read the graph from left to right!

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​The function to the right is negative on the intervals (-infinity, -3) and (-2,1).

​It is positive from (-3,-2) and (1, infinity).

​Increasing/Decreasing Intervals

Besides positive and negative, it can be interesting to tell when a function is increasing vs. decreasing.

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​The function to the right is increasing from (-infinity, -2.5ish) and (0, infinity).

​It is decreasing (sloping downward) from (-2.5, 0).

maximum and minimum

Often we want to know when the graph reaches a maximum or minimum value.

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​​The graph to the right has a local max at -2.5 with a value of about 1.

​​It also has a local minimum at 0 with a value of about -6.

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​A global max/min would be the highest or lowest point of the entire graph. This graph does not have those since it keeps going down forever to the left and up forever to the right.