Function Notation, Evaluating Functions, Domain & Range

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What is Function Notation?

Back

Function notation is a way to represent a function using symbols. It typically uses the format f(x), where 'f' is the name of the function and 'x' is the input variable.

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What does it mean to evaluate a function?

Back

Evaluating a function means substituting a specific value for the variable in the function's expression and calculating the result.

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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.

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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 find the domain of a function from a graph?

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To find the domain from a graph, identify the x-values that the graph covers. Look for the leftmost and rightmost points of the graph.

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How do you find the range of a function from a graph?

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To find the range from a graph, identify the y-values that the graph covers. Look for the lowest and highest points of the graph.

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Given f(x) = 2x + 3, what is f(4)?

Back

f(4) = 2(4) + 3 = 8 + 3 = 11.

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If g(x) = x^2, what is g(-3)?

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g(-3) = (-3)^2 = 9.

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What is the difference between a function and a relation?

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A function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value).

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What does it mean if a function is undefined at a certain point?

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A function is undefined at a certain point if there is no output value for that input, often due to division by zero or taking the square root of a negative number.