Final answer:
In mathematics, increasing and decreasing functions relate to the slope of a line or curve and its behavior on a graph. A decreasing line means y-values drop as we move from left to right, while in an increasing line, they rise. Constants are lines where the y-values do not change as we move along the x-values.
Step-by-step explanation:
Understanding Increasing and Decreasing Functions
When describing the behavior of a function or a line on a graph, we often use terms like increasing, decreasing, and constant. An increasing line means that as you move from left to right, the y-values are going up. Conversely, a decreasing line means that the y-values are going down as you move from left to right. When a line is constant, the y-values stay the same regardless of the x-values.
For example, if we have Line A as a decreasing line that is much steeper than Line B, which is an increasing line, this means that Line A's values drop more rapidly than the values of Line B rise. In another case, if Line B is a decreasing line while Line A is an increasing line, with Line B being steeper, it signifies that Line B's values decrease more quickly than the values of Line A increase.
To remember the direction of shifts for lines and curves on graphs, recall that a 'left shift' signifies a decrease, while a 'right shift' indicates an increase. This mnemonic helps: Less is associated with Left, and More is associated with Right. Additionally, when analyzing the behavior of curves, such as in economic graphs, check that a decreased curve means a lower quantity at any given price, and an increased curve means a higher quantity at any price.