Answer:
1. **If 'a' is positive:**
- When 'a' is positive, it typically results in the graph shifting either upwards or downwards depending on the specific function being used. For example, in a linear function like y = ax + b, if 'a' is positive, the graph will have a positive slope, moving upwards from left to right.
2. **If 'a' is negative:**
- If 'a' is negative, the graph will shift in the opposite direction compared to when 'a' is positive. Using the same linear function as an example, if 'a' is negative, the graph will have a negative slope, moving downwards from left to right.
3. **If 'a' increases:**
- Increasing the value of 'a' in a function can lead to a steeper graph, faster rate of change, or a different shape depending on the function. For instance, in a quadratic function like y = ax^2, increasing 'a' will affect the width and direction of the parabola.
4. **If 'a' decreases:**
- Conversely, decreasing 'a' in a function can flatten the graph, slow down the rate of change, or alter the shape as well. Using the same quadratic function example, decreasing 'a' in y = ax^2 can widen the parabola.
By understanding these relationships between the value of 'a' and the characteristics of the graphs, you can compare and analyze how changes in 'a' impact the overall shape, direction, and behavior of the graphs in your Maths Investigation.
Step-by-step explanation:
