Linear vs Exponential Functions

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What is a linear function?

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

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What is an exponential function?

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An exponential function is a function in which an independent variable appears in the exponent. It has the form f(x) = a * b^x, where a is a constant, b is the base, and x is the exponent.

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How can you identify a linear function from a table of values?

Back

A linear function will have a constant rate of change, meaning the difference between consecutive y-values is the same.

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How can you identify an exponential function from a table of values?

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An exponential function will have a constant ratio of change, meaning the ratio of consecutive y-values is the same.

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What does it mean for a function to be increasing?

Back

A function is increasing if, as the input (x) increases, the output (y) also increases.

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What does it mean for a function to be decreasing?

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A function is decreasing if, as the input (x) increases, the output (y) decreases.

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What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the change in y to the change in x, often represented as 'm' in the equation y = mx + b.

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What is the y-intercept of a linear function?

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The y-intercept is the point where the graph of the function crosses the y-axis, represented as 'b' in the equation y = mx + b.

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What is the growth factor in an exponential function?

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The growth factor is the base 'b' in the exponential function f(x) = a * b^x, which determines how quickly the function grows.

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What is a common example of a linear function in real life?

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A common example is calculating the total cost of items at a fixed price, where the cost increases linearly with the number of items.