Comparing Two Functions Represented in Different Ways

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What does it mean for a function to be linear?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the y-intercept of a function?

Back

The y-intercept is the point where the graph of a function crosses the y-axis, represented as (0, y).

Front

What is the rate of change in a function?

Back

The rate of change is the ratio of the change in the output value to the change in the input value, often represented as the slope in linear functions.

Front

How can you determine if a function is increasing?

Back

A function is increasing if, as the input values increase, the output values also increase.

Front

What is an exponential function?

Back

An exponential function is a function of the form y = ab^x, where a is a constant, b is a positive real number, and x is the exponent.

Front

What does it mean for two functions to have the same y-intercept?

Back

Two functions have the same y-intercept if they cross the y-axis at the same point, meaning they have the same output value when the input is 0.

Front

What is a multiplying pattern in functions?

Back

A multiplying pattern in functions refers to a relationship where the output is obtained by multiplying the input by a constant factor.

Front

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

Back

You can compare the rates of change by looking at the slopes of the functions; the function with the greater slope has a greater rate of change.

Front

What is the significance of the slope in a linear function?

Back

The slope indicates the steepness of the line and the direction of the function; a positive slope means the function is increasing, while a negative slope means it is decreasing.