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 an exponential function?

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An exponential function is a mathematical function of the form y = 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 quadratic function?

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

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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 have a constant rate of change, meaning the difference between consecutive y-values is the same for equal intervals of x.

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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 multiplicative rate of change, meaning each y-value is a constant multiple of the previous y-value for equal intervals of x.

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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 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 constant first difference indicate about a function?

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A constant first difference indicates that the function is linear.

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What does a constant second difference indicate about a function?

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A constant second difference indicates that the function is quadratic.