Solving 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

To evaluate a function means to calculate the output of the function for a given input.

Front

What is the notation for a function?

Back

Functions are typically denoted by letters such as f, g, or h, followed by parentheses containing the input value, e.g., f(x).

Front

How do you find the value of f(x) when f(x) = -x + 3?

Back

Substitute the value of x into the equation. For example, if x = 4, then f(4) = -4 + 3 = -1.

Front

What is the solution to the equation f(x) = 7 when f(x) = -x + 3?

Back

Set -x + 3 = 7, then solve for x: -x = 7 - 3, so x = -4.

Front

How do you solve for x in the equation f(x) = -5 when f(x) = x + 3?

Back

Set x + 3 = -5, then solve for x: x = -5 - 3, so x = -8.

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 linear function?

Back

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

Front

What does the slope of a function represent?

Back

The slope of a 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).