Linear, Quadratic, Exponential

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What is a linear function?

Back

A linear function is a function that graphs to a straight line. 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 is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

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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 the base (a positive real number), and x is the exponent.

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What does the graph of a linear function look like?

Back

The graph of a linear function is a straight line that can slope upwards or downwards depending on the sign of the slope.

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What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the leading coefficient (a).

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What does the graph of an exponential function look like?

Back

The graph of an exponential function shows rapid growth or decay, characterized by a curve that rises steeply or falls sharply.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base of the exponential function is greater than 1, leading to increasing values. Exponential decay occurs when the base is between 0 and 1, leading to decreasing values.

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How can you identify a linear function from a set of points?

Back

A set of points represents a linear function if the change in y divided by the change in x (slope) is constant between any two points.

Front

How can you identify a quadratic function from its graph?

Back

A quadratic function can be identified by its parabolic shape, which has a vertex and may have a maximum or minimum point.

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How can you identify an exponential function from its graph?

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An exponential function can be identified by its rapid increase or decrease, with the rate of change increasing or decreasing exponentially.