Functions, Domain, and Range

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

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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.

Front

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.

Front

How can you determine if a relation is a function?

Back

A relation is a function if every input (x-value) corresponds to exactly one output (y-value). This can be checked using the vertical line test.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, and it has the form y = mx + b, where m is the slope and b is the y-intercept.

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What is a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed. Examples include quadratic, exponential, and radical functions.

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What does it mean for y to be a function of x?

Back

It means that for every value of x, there is exactly one corresponding value of y.

Front

What is the notation for domain?

Back

The domain is often expressed in interval notation, such as (-10, 3) or using set notation like {x | -10 < x < 3}.

Front

What is the notation for range?

Back

The range is expressed similarly to the domain, using interval notation or set notation, such as {y | y > 0}.

Front

What is a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n are constants and n is a non-negative integer.