56.7k views
4 votes
Does a function decreasing imply it is negative? Does a function increasing imply it is positive? If not, draw a counter example.

User Mattimatti
by
7.0k points

1 Answer

2 votes

Final answer:

A decreasing function does not necessarily mean it is negative, and an increasing function does not necessarily mean it is positive; this is exemplified by a negative slope line that starts positive and a positive slope line that starts negative. The look of a slope varies with positive slopes rising, negative slopes falling, and zero slopes being horizontal.

Step-by-step explanation:

A function decreasing does not imply that it is negative, and a function increasing does not imply that it is positive. For example, a function may be decreasing yet still be above the x-axis, which means it is positive. Similarly, a function can be increasing and still have values that are below the x-axis, indicating negative values.

Consider a line represented by y = 5 - x. This line has a negative slope and is decreasing, but when x is between 0 and 5, y is positive. Now consider the line y = x - 5. This line has a positive slope and is increasing, but when x is between 0 and 5, y is negative.

Lastly, the appearance of a slope on a graph can be identified as follows: A positive slope indicates the line rises from left to right. A negative slope indicates the line falls from left to right. A slope of zero indicates a horizontal line, which does not rise or fall as it moves from left to right.

User Gaurav Adurkar
by
8.0k points