Graphing Exponential Functions: Understanding the Gradient Function

The video tutorial explores the gradient function of exponential graphs, focusing on y=a^x. It explains how the gradient increases with the value of 'a' and analyzes specific cases like y=2^x and y=3^x. The tutorial derives a general rule for calculating the gradient using a constant, and concludes with a derivation from first principles.

Explain why all exponential graphs pass through the point (0, 1).

What is the significance of the x-axis asymptote in exponential functions?

What happens to the gradient of the function as the value of 'a' increases?

Describe how the gradient changes as you move along the curve of y = 2^x.

What is the relationship between the gradient and the y-value in exponential functions?

How can you determine the gradient at a specific point on the graph of y = 3^x?

What is the formula for calculating the gradient at any point on the curve y = a^x?

Discuss the process of finding the gradient between two points on an exponential curve.

What does it mean for the gradient to be a constant value in the context of exponential functions?

How does the gradient function relate to the original function in exponential growth?