Comparing Functions REVIEW

Front

What is the equation for the total cost of x pounds of fruit if Lee charges $3 for a basket and $2.50 for each pound?

Back

y = 2.50x + 3

Front

What type of model fits the data collection {(-2,5), (-1, 2), (0, 1), (1, 2), (2, 5)}?

Back

Quadratic, because the second difference is constant

Front

What type of function is f(x) = 2(x+4)² - 7?

Back

Quadratic

Front

How can you determine if a graph is linear, exponential, or quadratic?

Back

Look at the rate of change: linear has a constant rate, exponential grows or decays rapidly, quadratic has a parabolic shape.

Front

What is the rate of change for a linear function?

Back

The rate of change is constant and is represented by the slope.

Front

What is the general form of a quadratic function?

Back

f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What does it mean for a function to be exponential?

Back

An exponential function has a constant ratio of change, typically in the form f(x) = ab^x.

Front

What is the difference between linear and quadratic functions?

Back

Linear functions graph as straight lines, while quadratic functions graph as parabolas.

Front

What is the significance of the second difference in a set of data points?

Back

If the second difference is constant, the data can be modeled by a quadratic function.

Front

How do you identify the rate of change in an exponential function?

Back

The rate of change increases or decreases rapidly, depending on whether the base is greater than or less than 1.