Increasing, Decreasing, and Constant Functions
This Grade 8 math skill from Pengi Math (Grade 8) teaches students to identify whether a function is increasing, decreasing, or constant over an interval. Students analyze graphs and tables to determine whether the output values rise, fall, or remain the same as the input values increase.
Key Concepts
Property The slope determines if the function is an increasing linear function, a decreasing linear function, or a constant function. $$y = mx + b \text{ is an increasing function if } m 0.$$ $$y = mx + b \text{ is a decreasing function if } m < 0.$$ $$y = mx + b \text{ is a constant function if } m = 0.$$.
Examples The function $y = 2x + 5$ is increasing because the slope $m=2$ is positive. The function $y = 3x + 1$ is decreasing because the slope $m= 3$ is negative. The function $y = 9$ is constant because the slope $m=0$. Its graph is a horizontal line.
Explanation The sign of the slope tells you the direction of the line. A positive slope means the line goes uphill from left to right. A negative slope means it goes downhill. A zero slope means the line is perfectly flat.
Common Questions
What does it mean for a function to be increasing?
A function is increasing on an interval when its output values get larger as the input values increase—the graph slopes upward from left to right.
What does it mean for a function to be decreasing?
A function is decreasing on an interval when its output values get smaller as the input values increase—the graph slopes downward from left to right.
What is a constant function?
A constant function is one where the output value does not change regardless of the input—the graph is a horizontal line.
How do you identify increasing and decreasing intervals from a graph?
Read the graph from left to right. Where the graph goes up, the function is increasing. Where it goes down, it is decreasing. Where it is flat, it is constant.
Where is this skill taught in Grade 8?
Increasing, decreasing, and constant functions are covered in the Grade 8 Pengi Math textbook under functions and their properties.