Function Review

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x-value, there is one and only one y-value.

Front

What is the definition of 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 is a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line. Its rate of change is not constant.

Front

How can you determine if a set of ordered pairs is a function?

Back

A set of ordered pairs is a function if no two pairs have the same first element (x-value).

Front

What is the constant rate of change in a linear function?

Back

The constant rate of change in a linear function is the slope (m), which represents how much the y-value changes for a unit change in the x-value.

Front

Evaluate f(-2) if f(x) = x^2 + 3.

Back

f(-2) = (-2)^2 + 3 = 4 + 3 = 7.

Front

What does it mean for a function to be 'not a function'?

Back

A relation is 'not a function' if at least one input (x-value) is associated with more than one output (y-value).

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation f(x) = mx + b.

Front

What is the difference between a function and a relation?

Back

A relation is any set of ordered pairs, while a function is a specific type of relation where each input has exactly one output.