Linear vs. Exponential vs. Quadratic Functions

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What is a linear function?

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A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

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What is an exponential function?

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An exponential function is a function in which an independent variable appears in the exponent. It can be expressed in the form y = a * b^x, where a is a constant, b is the base, and x is the exponent.

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What is a quadratic function?

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A quadratic function is a polynomial function of degree 2, which can be expressed in the form y = ax^2 + bx + c, where a, b, and c are constants.

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What does it mean for a function to be linear?

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A function is linear if it has a constant rate of change, meaning that the difference in y-values divided by the difference in x-values is the same for any two points on the graph.

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What does it mean for a function to be exponential?

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A function is exponential if it grows or decays at a rate proportional to its current value, meaning that the function's output increases or decreases multiplicatively.

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What does it mean for a function to be quadratic?

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

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

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A linear function will have a constant difference between consecutive y-values when the x-values are equally spaced.

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

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An exponential function will have a constant ratio between consecutive y-values when the x-values are equally spaced.

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How can you identify a quadratic function from a table of values?

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A quadratic function will have a constant second difference in the y-values when the x-values are equally spaced.

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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 Ax + By = C, where A, B, and C are constants.