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 is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x). It indicates how much y changes for a unit change in x.

Front

What is the y-intercept?

Back

The y-intercept is the point where the graph of a function crosses the y-axis. It occurs when x = 0.

Front

What is the x-intercept?

Back

The x-intercept is the point where the graph of a function crosses the x-axis. It occurs when y = 0.

Front

What does it mean for a relation to be a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value). No x-value can be paired with more than one y-value.

Front

How do you determine 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, based on its domain.

Front

What is end behavior in graphing?

Back

End behavior describes how the values of a function behave as x approaches positive or negative infinity. It helps in understanding the overall direction of the graph.

Front

What is a vertical line test?

Back

The vertical line test is a method used to determine if a relation is a function. If any vertical line intersects the graph at more than one point, it is not a function.

Front

What is a constant function?

Back

A constant function is a linear function where the slope is zero, meaning it produces the same output (y-value) for every input (x-value). Its graph is a horizontal line.

Front

What is the difference between discrete and continuous functions?

Back

Discrete functions have distinct, separate values (often represented as points), while continuous functions have an unbroken line or curve, allowing for any value within a range.