Identifying Constant Intervals
A function is constant on an interval when the output (y-value) stays the same as the input (x-value) increases. On a graph, a constant interval appears as a perfectly horizontal line segment. A temperature graph holding steady at 20 degrees C from hour 3 to hour 5 shows a constant interval on 3 less than or equal to x less than or equal to 5. A hiker walking along a flat plateau from mile 2 to mile 3 shows a constant altitude interval. Identifying constant intervals from enVision Mathematics, Grade 8, Chapter 3 helps students describe the full behavior of a function in 8th grade math.
Key Concepts
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.
Common Questions
What is a constant interval on a graph?
A constant interval is a section of the graph where the y-value (output) stays the same as x increases. It appears as a flat, horizontal line segment.
How do I identify a constant interval on a function graph?
Look for horizontal sections where the graph is perfectly flat. The x-values where this occurs form the constant interval.
Why is a horizontal line segment called constant?
Because height (the y-value) does not change as you move left to right along it. The quantity being measured is neither increasing nor decreasing.
A graph is horizontal from x = 2 to x = 5 at y = 10. What is the constant interval?
The constant interval is 2 less than or equal to x less than or equal to 5. During this interval, the output stays fixed at 10.
How is a constant interval different from a decreasing interval?
In a constant interval the graph is horizontal (slope = 0). In a decreasing interval the graph slopes downward (negative slope).
When do 8th graders learn about constant intervals?
Chapter 3 of enVision Mathematics, Grade 8 covers this in the Use Functions to Model Relationships unit.