Topic 2A Test Prep #2

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What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined. For example, the domain of the function f(x) = 1/x is all real numbers except x = 0.

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What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce. For example, the range of the function f(x) = x^2 is all non-negative real numbers, i.e., [0, ∞).

Front

How do you determine the domain of a function given its equation?

Back

To determine the domain of a function, identify any restrictions on the input values. For example, for f(x) = √(x-1), the domain is x ≥ 1 because the expression under the square root must be non-negative.

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What is an interval notation?

Back

Interval notation is a way of writing subsets of the real number line. For example, (a, b) represents all numbers between a and b, not including a and b, while [a, b] includes a and b.

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What does it mean for a function to be continuous?

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A function is continuous if there are no breaks, jumps, or holes in its graph. Formally, a function f(x) is continuous at a point x = c if lim (x→c) f(x) = f(c).

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What is the difference between open and closed intervals?

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An open interval (a, b) does not include its endpoints a and b, while a closed interval [a, b] includes both endpoints.

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How do you find the range of a function?

Back

To find the range of a function, analyze the output values for all possible input values. This can involve graphing the function or solving inequalities.

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What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as x approaches a. It indicates that the function is undefined at x = a.

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What is a horizontal asymptote?

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A horizontal asymptote is a line y = b that a function approaches as x approaches infinity or negative infinity. It indicates the behavior of the function at extreme values.

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What is the significance of the x-intercept?

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The x-intercept of a function is the point where the graph crosses the x-axis. It represents the value of x for which f(x) = 0.