EVALUATING FUNCTIONS

Front

What is a function in mathematics?

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.

Front

How do you evaluate a function at a given point?

Back

To evaluate a function at a given point, substitute the input value into the function's equation and simplify to find the output.

Front

What does it mean for a function to be linear?

Back

A linear function is a function that can be graphically represented as a straight line, typically in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input is associated with exactly one output, while a relation can have multiple outputs for a single input.

Front

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

What is a composite function?

Back

A composite function is formed when one function is applied to the result of another function, denoted as (f ∘ g)(x) = f(g(x)).

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What is the vertical line test?

Back

The vertical line test is a method used to determine if a curve is a function; if a vertical line intersects the curve at more than one point, it is not a function.

Front

What is an inverse function?

Back

An inverse function reverses the effect of the original function, such that if f(x) = y, then f⁻¹(y) = x.

Front

How do you find the x-intercept of a function?

Back

To find the x-intercept of a function, set the output (y) to zero and solve for the input (x).