Lesson 17: Form Follows Function

Front

What is the definition of a continuous function?

Back

A continuous function is a function that can be graphed without lifting the pencil from the paper, meaning there are no breaks, jumps, or holes in the graph.

Front

What is the definition of a discrete function?

Back

A discrete function is a function that consists of distinct or separate values, often represented as individual points on a graph.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function, indicating how much the output (y) changes for a given change in the input (x).

Front

How do you determine if a function is continuous or discrete from its graph?

Back

If the graph is unbroken and can be drawn without lifting the pencil, it is continuous. If it consists of separate points, it is discrete.

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, indicating the value of the function when x = 0.

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as the input (x) increases, the output (y) also increases.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as the input (x) increases, the output (y) decreases.

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

How do you find the common ratio in a geometric sequence?

Back

The common ratio is found by dividing any term in the sequence by the previous term.

Front

What is the formula for a linear function?

Back

The formula for a linear function is typically written as y = mx + b, where m is the slope and b is the y-intercept.