Functions - Evaluating Functions

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.

Front

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 to find the corresponding output.

Front

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

Back

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

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

How do you find the value of a function at a given point?

Back

To find the value of a function at a given point, substitute the x-value into the function's equation and simplify.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, typically in the form f(x) = mx + b.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function; it indicates how much the output (y) changes for a unit change in the input (x).

Front

What is the y-intercept of a function?

Back

The y-intercept of a function is the point where the graph of the function crosses the y-axis, represented as (0, f(0)).

Front

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

Back

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