4.5 Comparing Functions

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 the rate of change in a function represent?

Back

The rate of change represents how much the output of a function changes for a given change in the input. It is often expressed as a ratio.

Front

How do you determine which function has a greater rate of change?

Back

To determine which function has a greater rate of change, compare the slopes of the functions if they are linear, or analyze the change in output over a specific interval.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the change in the y-value to the change in the x-value, often represented as 'm' in the equation y = mx + b.

Front

What does the y-intercept represent in a function?

Back

The y-intercept is the point where the function crosses the y-axis, representing the output value when the input is zero.

Front

How can you compare two linear functions?

Back

You can compare two linear functions by examining their slopes and y-intercepts to determine which function increases faster or has a higher starting value.

Front

What is the equation of a linear function?

Back

The equation of a linear function is typically written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

If Nate's service is described by y = 4x + 6, what is the cost for 8 movies?

Back

For 8 movies, the cost is y = 4(8) + 6 = 38.

Front

What is the significance of comparing costs in functions?

Back

Comparing costs in functions helps determine which option is more economical based on the given inputs.

Front

What does it mean if two functions have the same rate of change?

Back

If two functions have the same rate of change, it means they increase or decrease at the same rate, resulting in parallel lines when graphed.