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 a positive real number, and 'x' is the exponent. It represents growth or decay at a constant percentage rate.

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What is a quadratic function?

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A quadratic function is a polynomial function of degree 2, typically written 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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What is a linear function?

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A linear function is a polynomial function of degree 1, represented by the equation f(x) = mx + b, where 'm' is the slope and 'b' is the y-intercept.

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What does the graph of an exponential growth function look like?

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The graph of an exponential growth function rises rapidly and increases without bound as x increases, typically starting from a point above the x-axis.

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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 that opens upwards or downwards, depending on the sign of 'a' in the equation f(x) = ax^2 + bx + c.

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What does the graph of a linear function look like?

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The graph of a linear function is a straight line that can slope upwards or downwards, depending on the value of the slope 'm'.

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What is exponential decay?

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Exponential decay is a decrease in a quantity at a rate proportional to its current value, typically modeled by the function f(x) = a * e^(-bx), where 'a' and 'b' are constants.

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How can you identify a quadratic function from its equation?

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A quadratic function can be identified by the presence of the x^2 term in its equation, indicating that the highest degree of x is 2.

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What is the difference between linear and quadratic functions?

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Linear functions have a constant rate of change and produce straight-line graphs, while quadratic functions have a variable rate of change and produce parabolic graphs.

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What is the general form of an exponential growth equation?

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The general form of an exponential growth equation is y = a * b^x, where 'a' is the initial value and 'b' is the growth factor.