Linear + Exponential Functions Review

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What is the definition of a linear function?

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A linear function is a function that can be graphically represented in the Cartesian plane as a straight line. 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 the definition of 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. The graph of an exponential function is a curve that increases or decreases rapidly.

Front

How can you identify a linear function from its equation?

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A linear function can be identified by its equation, which will be in the form f(x) = mx + b. If the highest power of x is 1, it is linear.

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How can you identify an exponential function from its equation?

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An exponential function can be identified by its equation, which will be in the form f(x) = a * b^x. If the variable x is in the exponent, it is exponential.

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What is the difference between discrete and continuous data?

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Discrete data consists of distinct or separate values (e.g., number of students), while continuous data can take any value within a range (e.g., height, weight).

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What is an explicit equation?

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An explicit equation is a mathematical expression that defines a function directly in terms of its independent variable, allowing for the calculation of output values for given input values.

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What is the explicit equation for a linear function with a slope of 2 and a y-intercept of 1?

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f(x) = 2x + 1.

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What is the explicit equation for an exponential function with a base of 3 and a starting value of 2?

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f(x) = 2 * 3^x.

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How do you find the missing term in a linear sequence?

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To find the missing term in a linear sequence, identify the common difference between consecutive terms and add it to the previous term.

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What is the common difference in the sequence 1, 4, 7, 10, ...?

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The common difference is 3.