Identifying Linear Functions & Function Notation

Front

What is a linear function?

Back

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

Front

What does the notation f(x) represent?

Back

f(x) represents the output of the function f for a given input x. It is a way to express the relationship between the input and output of a function.

Front

How do you find the slope of a linear function?

Back

The slope (m) of a linear function can be found by taking the change in y (rise) over the change in x (run) between two points on the line.

Front

What is the y-intercept of a linear function?

Back

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

Front

If f(x) = 3/2 x - 4, what is f(0)?

Back

f(0) = 3/2(0) - 4 = -4.

Front

If f(x) = 3/2 x - 4, what is the input (x) if f(x) = 2?

Back

To find x, set 2 = 3/2 x - 4. Solving gives x = 4.

Front

What is the definition of 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 corresponding y-value.

Front

What does it mean for a function to be non-linear?

Back

A non-linear function is a function that does not create a straight line when graphed. Its rate of change is not constant.

Front

How can you tell if a graph represents a function?

Back

A graph represents a function if it passes the vertical line test, meaning that no vertical line intersects the graph at more than one point.

Front

If f(x) = 3/2 x - 4, what is the input (x) if f(x) = -1?

Back

To find x, set -1 = 3/2 x - 4. Solving gives x = 2.