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).

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

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

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

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

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

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

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

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

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

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