A function is a mathematical relationship between two variables, where each input has a unique output. It can be represented graphically as a line or curve.
A positive gradient, also known as a positive slope, is a line that increases in value from left to right. This means that as the x-values increase, the y-values also increase.
A negative gradient, also known as a negative slope, is a line that decreases in value from left to right. This means that as the x-values increase, the y-values decrease.
To draw a function with negative and positive gradient, start by selecting a range of x-values and plugging them into the function to get corresponding y-values. Plot these points on a graph and connect them with a line. For negative gradient, the line should decrease from left to right, and for positive gradient, the line should increase from left to right.
Considering both negative and positive gradient when sketching a function is important because it helps us understand the behavior of the function and how it changes in different areas. It also allows us to identify key points, such as the slope at any given point, and make predictions about the function's behavior in other areas. Additionally, it helps us accurately represent the relationship between the two variables in a visual form.