Functions Practice

Front

What is a function in mathematics?

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

How can you determine if a diagram represents a function?

Back

A diagram represents a function if every vertical line drawn through the graph intersects it at most once (Vertical Line Test).

Front

What does it mean for a relationship to be linear and non-proportional?

Back

A linear relationship means that the graph of the relationship is a straight line, while non-proportional indicates that the line does not pass through the origin.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you graph the equation y = 1/2x - 3?

Back

To graph y = 1/2x - 3, start at the y-intercept (0, -3) and use the slope (1/2) to find another point by going up 1 unit and right 2 units.

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the slope, which represents how much the output value changes for a unit change in the input value.

Front

What is the initial value in a linear function?

Back

The initial value is the y-intercept of the function, representing the output value when the input is zero.

Front

How do you interpret the rate of change in a real-world context?

Back

The rate of change indicates how quickly one quantity changes in relation to another, such as speed or cost per unit.

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is significant because it shows the starting value of the dependent variable when the independent variable is zero.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input is associated with exactly one output, while a relation can have multiple outputs for a single input.