Graphs of Functions

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Add these definitions to your digital notebook

• Maximum: 1) the highest point on a graph, or 2) the biggest possible output of a function. Not all functions have a maximum

• Minimum: 1) the lowest point on a graph, or 2) the smallest possible output of a function. Not all functions have a minimum

• Increasing: a graph or part of a graph that goes up from left to right

• Decreasing: a graph or part of a graph that goes down from left to right

• x-intercept: the point(s) where the graph crosses the x-axis (where y is 0). A function can have any number of x-intercepts

• y-intercept: the point where the graph crosses the y-axis (where x is 0). A function has at most one y-intercept

• Domain: all the possible inputs (x-values) for a function

• Range: all the possible outputs (y-values) for a function

Draw

Mark the maximum on the graph. If there isn't one, write N/A

Open Ended

What are the coordinates of the maximum?

Draw

Mark the minimum on the graph. If there isn't one, write N/A

Open Ended

What are the coordinates of the minimum?

Draw

Mark the x-intercept(s) on the graph. If there isn't one, write N/A

Draw

Mark the y-intercept on the graph. If there isn't one, write N/A

Open Ended

What are the coordinates of the y-intercept?

Draw

Highlight any increasing intervals

Open Ended

List all increasing intervals

Example: 5 seconds to 9 seconds

Draw

Highlight any decreasing intervals

Open Ended

List all decreasing intervals

Example: 0 seconds to 5 seconds

Open Ended

What is the domain of the graph?

Open Ended

What is the range of the graph?

Multiple Choice

The graph shows the number of homeless Americans each year from 2007 to 2023.

Which feature of the graph would help us find when homelessness was lowest?

• the maximum

• the minimum

• the y-intercept

• the domain

Multiple Choice

The graph shows the number of homeless Americans each year from 2007 to 2023.

Which feature of the graph would help us find the years when homelessness was going down?

• increasing intervals

• the minimum

• decreasing intervals

• the domain

Multiple Choice

The graph shows the number of homeless Americans each year from 2007 to 2023.

Which feature of the graph would help us find the years no one was homeless?

• the y-intercept

• the minimum

• the x-intercept

• decreasing intervals

Open Ended

The graph shows the number of homeless Americans each year from 2007 to 2023.

What was the highest homeless population from 2007 to 2023, and in what year did it happen?

Open Ended

The graph shows the number of homeless Americans each year from 2007 to 2023.

During what years was homelessness increasing?

Open Ended

The graph shows the number of homeless Americans each year from 2007 to 2023.

Were there any years when no one was homeless?