Math 3: EOC Review Unit 1 - Function Basics

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What is a function?

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A function is a relation that assigns exactly one output for each input. In mathematical terms, if f is a function, then for every x in the domain, there is a unique y in the range such that y = f(x).

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What is the domain of a function?

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The domain of a function is the set of all possible input values (x-values) for which the function is defined.

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What is the range of a function?

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The range of a function is the set of all possible output values (y-values) that the function can produce.

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How do you determine if a set of values is a function?

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A set of values is a function if no two ordered pairs have the same first element (x-value).

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What is the notation for the inverse of a function?

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The inverse of a function f is denoted as f^{-1}. It reverses the roles of inputs and outputs.

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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, swap the x and y in the equation and solve for y.

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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 f(x) = mx + b, where m is the slope and b is the y-intercept.

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What is the slope of a line?

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The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

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What is a vertical line test?

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The vertical line test is a method to determine if a curve is a function. If any vertical line intersects the curve more than once, it is not a function.

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What is an absolute value function?

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An absolute value function is a function that outputs the distance of a number from zero, defined as f(x) = |x|.