Linear vs Exponential Functions

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What is an exponential function?

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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 multiplies the same base number (b) for each unit increase in x.

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What is a linear function?

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A linear function is a mathematical function of the form f(x) = mx + b, where 'm' is the slope and 'b' is the y-intercept. It adds a constant value (m) for each unit increase in x.

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

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An exponential function will show a constant multiplicative rate of change between consecutive values, meaning the ratio of successive outputs is constant.

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

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A linear function will show a constant additive rate of change between consecutive values, meaning the difference between successive outputs is constant.

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What is the general form of a linear equation?

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The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

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What is the general form of an exponential equation?

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The general form of an exponential equation is y = a * b^x, where a is a constant, b is the base, and x is the exponent.

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What type of function is represented by the equation y = 3 * 2^x?

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Exponential function.

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What type of function is represented by the equation y = 5x + 2?

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Linear function.

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If a function doubles its output for each increase of 1 in the input, what type of function is it?

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Exponential function.

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If a function increases by a constant amount for each increase of 1 in the input, what type of function is it?

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Linear function.