2.2.2 Interpret and Compare Functions

Front

What is an initial value in a function?

Back

The initial value is the starting point of a function, often represented as the y-intercept in a linear function.

Front

How do you determine the rate of change in a linear function?

Back

The rate of change is determined by the slope of the line, which is calculated as the change in y divided by the change in x.

Front

What does a constant slope indicate about a function?

Back

A constant slope indicates that the function is linear, meaning it has a consistent rate of change.

Front

If a function has a slope of 2, what does this mean?

Back

It means that for every 1 unit increase in x, the value of y increases by 2 units.

Front

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

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

In the context of a phone payment plan, what does the rate of change represent?

Back

The rate of change represents the amount paid per month, which is a constant value in this case.

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, representing the initial value of the function.

Front

How can you compare the initial values of two functions?

Back

You can compare initial values by evaluating the functions at x = 0 or by looking at their y-intercepts.

Front

What does it mean if a function is non-linear?

Back

A non-linear function does not have a constant rate of change; its slope varies at different points.

Front

If a function starts at 60 points and gains 1 point per assignment, what is its initial value?

Back

The initial value is 60 points.