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 of a function represent?

Back

The rate of change of a function represents how much the output value changes for a change in the input value, often described as the slope of the function.

Front

How do you determine the greatest rate of change among functions?

Back

To determine the greatest rate of change, compare the slopes of the functions; the function with the steepest slope has the greatest rate of change.

Front

What is a y-intercept?

Back

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

Front

How can you identify the smallest initial value of a function?

Back

The smallest initial value can be identified by evaluating the function at its starting point, usually when the input is zero.

Front

What is the significance of comparing functions?

Back

Comparing functions helps to understand their behaviors, such as growth rates, initial values, and overall trends.

Front

What is a linear function?

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 difference between a function's initial value and its y-intercept?

Back

The initial value refers to the starting output of a function at a specific input, while the y-intercept is specifically the output when the input is zero.

Front

How do you find the slope of a linear function?

Back

The slope of a linear function can be found by taking the difference in the y-values divided by the difference in the x-values between two points on the line.

Front

What does it mean for a function to have a positive slope?

Back

A function with a positive slope increases as the input increases, indicating a direct relationship between the input and output.