AP Precalculus: Unit 2 Review

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What is a residual plot?

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A residual plot is a graph that shows the residuals on the vertical axis and the independent variable on the horizontal axis. It helps to assess the fit of a regression model.

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What does it mean if a residual plot shows a random scatter?

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A random scatter in a residual plot indicates that a linear regression model is appropriate for the data.

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What is a geometric series?

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A geometric series is the sum of the terms of a geometric sequence, where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

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How do you find the sum of a geometric series?

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The sum of the first n terms of a geometric series can be calculated using the formula: S_n = a(1 - r^n) / (1 - r), where a is the first term and r is the common ratio.

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What is function composition?

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Function composition is the process of applying one function to the results of another function. If f and g are two functions, the composition is denoted as f(g(x)).

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How do you find the composition of two functions?

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To find the composition of two functions f and g, substitute g(x) into f. For example, if f(x) = 2x and g(x) = 2x^2 - 1, then f(g(x)) = f(2x^2 - 1) = 2(2x^2 - 1).

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What is the inverse of a function?

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The inverse of a function f, denoted as f^{-1}, is a function that reverses the effect of f. If f(x) = y, then f^{-1}(y) = x.

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How do you find the inverse of a function algebraically?

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To find the inverse of a function algebraically, swap the x and y in the equation and solve for y.

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