Q: How can you determine the intersection points of two functions' graphs?

To find the intersection points of two functions' graphs, you need to set their equations equal to each other and solve for x. This will give you the x-coordinates of the intersection points. Substitute these x-values back into either of the original equations to find the corresponding y-values. These (x, y) pairs are the intersection points.

Q: What is the significance of the slope in the graph of a function?

The slope of a function's graph indicates the rate of change of the dependent variable (usually y) with respect to the independent variable (usually x). In a linear function, the slope is constant and represents the steepness and direction of the line. A positive slope means the line rises as x increases, while a negative slope means it falls. Understanding the slope is essential for interpreting and predicting the behavior of functions.

Question 1

What is a graph of a function in the context of Edexcel IGCSE Mathematics?

Accepted Answer

In Edexcel IGCSE Mathematics, a graph of a function is a visual representation of the relationship between two variables, typically x and y. It shows how the value of y changes in response to changes in x. This is crucial for understanding how different types of functions behave, such as linear, quadratic, and exponential functions.

Question 2

How do you plot the graph of a linear function?

Accepted Answer

To plot the graph of a linear function, you first need to identify the equation of the line, usually in the form y = mx + c, where m is the slope and c is the y-intercept. Start by plotting the y-intercept on the y-axis. Then, use the slope to determine another point on the line by rising and running from the y-intercept. Connect these points with a straight line.

Question 3

What are the key features of a quadratic function's graph?

Accepted Answer

The graph of a quadratic function, typically in the form y = ax^2 + bx + c, is a parabola. Key features include the vertex, which is the highest or lowest point, the axis of symmetry, which is a vertical line through the vertex, and the direction of the parabola, which opens upwards if a > 0 and downwards if a < 0. The roots or x-intercepts, where the graph crosses the x-axis, are also significant.

Question 4

How can you determine the intersection points of two functions' graphs?

Accepted Answer

To find the intersection points of two functions' graphs, you need to set their equations equal to each other and solve for x. This will give you the x-coordinates of the intersection points. Substitute these x-values back into either of the original equations to find the corresponding y-values. These (x, y) pairs are the intersection points.

Question 5

What is the significance of the slope in the graph of a function?

Accepted Answer

The slope of a function's graph indicates the rate of change of the dependent variable (usually y) with respect to the independent variable (usually x). In a linear function, the slope is constant and represents the steepness and direction of the line. A positive slope means the line rises as x increases, while a negative slope means it falls. Understanding the slope is essential for interpreting and predicting the behavior of functions.

Graph of Functions

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