Function Type From Tables

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What is a linear function?

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A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

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What is a quadratic function?

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A quadratic function is a polynomial function of degree 2, typically in the form y = ax² + bx + c, where a, b, and c are constants. Its graph is a parabola.

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What is an exponential function?

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An exponential function is a mathematical function of the form y = ab^x, where a is a constant, b is the base, and x is the exponent. It grows rapidly as x increases.

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What is a logarithmic function?

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A logarithmic function is the inverse of an exponential function, typically in the form y = log_b(x), where b is the base. It grows slowly compared to linear and exponential functions.

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

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A linear function will show a constant rate of change between the x and y values, meaning the difference in y values divided by the difference in x values is constant.

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

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A quadratic function will show a constant second difference in the y values when the x values are evenly 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 show a constant ratio of change between consecutive y values when the x values are evenly spaced.

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

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A logarithmic function will show a decreasing rate of change in y values as x increases, often appearing as a curve that flattens out.

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What does a +1 pattern in x values indicate?

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A +1 pattern in x values indicates that the x values are increasing by 1 unit, which is common in linear functions.

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What does a -3 pattern in y values indicate?

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A -3 pattern in y values indicates that the y values are decreasing by 3 units, which can suggest a linear relationship.