Linear vs Exponential Functions

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What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where 'a' is a constant, 'b' is a positive real number, and 'x' is the exponent. It shows growth or decay at a constant percentage rate.

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What is a linear function?

Back

A linear function is a function that creates a straight line when graphed. It can be expressed in the form f(x) = mx + b, where 'm' is the slope and 'b' is the y-intercept.

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What does it mean for a function to multiply the same number each time?

Back

This describes an exponential function, where each output is a constant multiple of the previous output.

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What does it mean for a function to add the same number each time?

Back

This describes a linear function, where each output increases or decreases by a constant amount as the input increases.

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How can you identify an exponential function from a graph?

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An exponential function graph shows a rapid increase or decrease, forming a curve that gets steeper as it moves away from the origin.

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How can you identify a linear function from a graph?

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A linear function graph is a straight line, indicating a constant rate of change between the x and y values.

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What is the general form of an exponential equation?

Back

The general form is y = a * b^x, where 'a' is the initial value and 'b' is the growth factor.

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What is the general form of a linear equation?

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The general form is y = mx + b, where 'm' is the slope and 'b' is the y-intercept.

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What is the slope in a linear function?

Back

The slope (m) represents the rate of change of the function, indicating how much y changes for a unit change in x.

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What is the y-intercept in a linear function?

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The y-intercept (b) is the value of y when x is 0, representing where the line crosses the y-axis.