Comparing, Describing, & Constructing 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 y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent in a linear function?

Back

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

Front

What is the y-intercept in a linear function?

Back

The y-intercept (b) is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

How do you determine if one linear function is cheaper than another?

Back

To determine if one linear function is cheaper, compare the outputs (costs) of both functions for the same input (quantity of items or services).

Front

What is the formula for calculating the cost of a service based on a linear function?

Back

The cost can be calculated using the formula y = mx + b, where y is the total cost, m is the cost per item, x is the number of items, and b is the fixed cost.

Front

How do you construct a linear model from a graph?

Back

To construct a linear model from a graph, identify two points on the line, calculate the slope using the formula (y2 - y1)/(x2 - x1), and use one point to find the y-intercept.

Front

What is the significance of the initial fee in a service cost function?

Back

The initial fee is a fixed cost that must be paid regardless of the number of items or services used. It affects the total cost but does not change with quantity.

Front

How can you compare the rates of change of two functions?

Back

To compare the rates of change, calculate the slope of each function. The function with the greater slope has a higher rate of change.

Front

What does it mean for a function to have a greater rate of change?

Back

A function with a greater rate of change increases or decreases more rapidly than another function over the same interval.

Front

How can you represent a decrease in stock value over time graphically?

Back

A decrease in stock value over time can be represented by a downward sloping line on a graph, indicating a negative change in value.