Comparing Functions - LQE Honors

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 function represent?

Back

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

Front

What is a y-intercept?

Back

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

Front

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

Back

A function has a constant rate of change if its slope is the same between any two points on the graph. This is characteristic of linear functions.

Front

What is an exponential function?

Back

An exponential function is a function of the form f(x) = a(b)^x, where a is a constant, b is the base, and x is the exponent. It grows or decays at a multiplicative rate.

Front

How do you determine the greater rate of change between two functions?

Back

To determine the greater rate of change, compare the slopes of the two functions. The function with the larger slope has the greater rate of change.

Front

What does it mean for a function to increase at a multiplicative rate?

Back

A function increases at a multiplicative rate if its output grows by a constant factor for each unit increase in the input. This is typical of exponential functions.

Front

What is the significance of the maximum value of a function?

Back

The maximum value of a function is the highest point on its graph. It indicates the greatest output value that the function can achieve.

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions have a constant rate of change and graph as straight lines, while nonlinear functions have varying rates of change and can graph as curves.

Front

What does it mean for functions to be increasing?

Back

Functions are increasing if their output values rise as the input values increase. This means the slope is positive.