3.1 - 3.5 Linear Functions

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 slope of a line represent?

Back

The slope of a line represents the rate of change of the function. It indicates how much the y-value changes for a unit change in the x-value.

Front

What is the y-intercept of a linear function?

Back

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

Front

How do you determine if a relation is a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value). This can be checked using the vertical line test.

Front

What does d(4) = 37 mean in the context of Derek's earnings?

Back

It means that after working for 4 hours, Derek has earned a total of $37.

Front

What is the equation of a vertical line?

Back

The equation of a vertical line is of the form x = a, where 'a' is a constant.

Front

What is the equation of a horizontal line?

Back

The equation of a horizontal line is of the form y = b, where 'b' is a constant.

Front

What does the function p(x) = 5x + 12 represent?

Back

It represents the total number of pencils Ms. Brackemyer has after collecting pencils for x days, starting with 12 pencils and collecting 5 more each day.

Front

What does p(8) = 52 mean in the context of Ms. Brackemyer's pencil collection?

Back

It means that after collecting pencils for 8 days, Ms. Brackemyer has a total of 52 pencils.

Front

What is the difference between a function and a non-function?

Back

A function has one output for each input, while a non-function may have multiple outputs for a single input.