Linear, Exponential, Quadratic: Which is it?

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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 the base (a positive real number), and 'x' is the exponent. It shows rapid growth or decay.

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What is a linear function?

Back

A linear function is a function that graphs to a straight line, represented by the equation 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) = ax^2 + bx + c, where 'a', 'b', and 'c' are constants and 'a' is not zero.

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How can you identify exponential growth?

Back

Exponential growth can be identified by a graph that rises sharply and continuously increases as 'x' increases, typically represented by a base greater than 1.

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How can you identify exponential decay?

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Exponential decay is identified by a graph that decreases sharply and approaches zero as 'x' increases, typically represented by a base between 0 and 1.

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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?

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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 is the general form of a quadratic equation?

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The general form of a quadratic equation is y = ax^2 + bx + c, where 'a', 'b', and 'c' are constants.

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What is the vertex of a quadratic function?

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The vertex of a quadratic function is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

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What is the y-intercept of a linear function?

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The y-intercept of a linear function is the point where the graph crosses the y-axis, represented by the value of 'b' in the equation f(x) = mx + b.