Graph Vocabulary and Interpreting Graphs of Functions

Graph Vocabulary

Graph Vocabulary This one is also called a “constant” function dependent variable decreases as the independent variable increases both the independent and dependent variables increase This one is also called a “constant” function and a function

Parts of a graph… X-intercept – where the graph crosses the x-axis. Y-intercept – where the graph crosses the y-axis. (0, y)

Find the x- and y- intercepts of the graph. X-intercepts (-2, 0) and (2, 0) Y-intercept (0, -4)

Parts of a graph… Increasing Intervals – A function is “increasing” when the y-value (dependent variable) increases as the x-value (independent variable) increases. Interval – A section of the graph. This function is increasing for the interval shown. It may be increasing or decreasing elsewhere. Decreasing Intervals – A function is “decreasing” when the y-value (dependent variable) decreases as the x-value (independent variable) increases.

Find where the function is increasing or decreasing. To state an interval: [starting x value, ending x value] The graph is increasing in the following intervals: [-2.2, -1.2] [1.2, 2.2] The graph is decreasing in the following interval: [-1.2, 1.2]

Parts of a graph… Maximum – the largest value of the function within the interval. What is the maximum value in the interval [1, 5]? The maximum value is 4. Minimum – the smallest value of the function with an interval. What is the minimum value in the interval [1, 5]? The minimum value is 1.

Has an absolute max. Does not have absolute min. Parabolas (u shape) go on forever in one direction Parts of a graph… Absolute Maximum – a function has an absolute max. if there is a point whose y-coordinate is greater than the y of every other point on the graph The “highest” spot on the graph It doesn’t “go up forever” Absolute Minimum – a function has an absolute min. if there is a point whose y-coordinate is less than the y of every other point on the graph. The “lowest” spot on the graph It doesn't “go down forever” Has an absolute min. Does not have absolute max. Absolute value fcts (v shape) go on forever in one direction Doesn’t have an absolute max. or absolute min. Linear functions (lines) go on forever in each direction

Identify the features of the function. Find the x-intercepts: (-8, 0), (-3, 0), (8, 0) Find the y-intercept: (0, -4) Name the intervals where the function is increasing: [-8, -6], [6, ∞] Name the intervals where the function is decreasing: [-6, 0], [4, 6] Name the interval where the function is constant (flat): * Remember to write intervals by [starting x value, ending x value] [0, 4]

Identify the features of the function. Name the maximum for the interval [-8, -5]: 7 Name the minimum for the interval [2, 8]: -8