Sketch Exponential, Reciprocal and Cubic Graph
In this lesson, you will learn how to sketch exponential, reciprocal, and cubic graphs by understanding their key shapes and features. You will explore how exponential graphs grow or decay rapidly, how reciprocal graphs form two separate curves with asymptotes, and how cubic graphs create smooth curves with turning points or points of inflection.
Related Lessons:
What Is Asymptotes?
In this lesson, you will learn about asymptotes, which are lines that a graph approaches but never touches. You will explore vertical and horizontal asymptotes, understand how they help describe the behaviour of graphs. We will use them to sketch functions such as reciprocal and exponential graphs later.
Sketching Reciprocal Graph
In this lesson, you will learn how to sketch reciprocal graphs by understanding their key features, such as asymptotes, intercepts, and the shape of the curves in different quadrants. By recognising how the graph behaves near the axes and for small and large values of \(x\), you will be able to sketch reciprocal functions accurately by memorising only one standard graph.
Sketching Exponential Graph
In this lesson, you will learn how to sketch exponential graphs by understanding their key features, such as the y-intercept and the horizontal asymptote. By recognising the general shape and how the graph behaves for large and small values of x, you will be able to sketch exponential functions by memorising minimum number of graphs.
Sketching Cubic Graph
In this lesson, you will learn how to sketch cubic graphs by understanding their key features, such the standard “S” shape, intercepts, turning points, and points of inflection.