Unit 1 review - modeling 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 linear function represent?

Back

The slope of a linear function represents the rate of change of the function. It indicates how much the output (y) changes for a unit change in the input (x).

Front

How do you evaluate a function at a specific point?

Back

To evaluate a function f(x) at a specific point x = a, substitute a into the function: f(a).

Front

What is the y-intercept of a linear function?

Back

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

Front

What is the meaning of a flat rate in a function?

Back

A flat rate in a function indicates a constant charge that does not change with the input variable. In the function c(x) = 5x + 100, the flat rate is $100.

Front

How do you find the total cost using a linear function?

Back

To find the total cost using a linear function, substitute the value of the variable into the function. For example, c(x) = 5x + 100 gives the total cost based on miles driven.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the input (x) increases, the output (f(x)) also increases. This is indicated by a positive slope.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as the input (x) increases, the output (f(x)) decreases. This is indicated by a negative slope.

Front

How can you determine the slope from a graph?

Back

The slope can be determined by selecting two points on the line and using the formula: slope = (change in y) / (change in x).

Front

What is the formula for finding the slope between two points (x1, y1) and (x2, y2)?

Back

The formula for finding the slope is: slope = (y2 - y1) / (x2 - x1).