Function Notation in Context

Front

What does the function notation B(t) represent in the context of Tyler's bathtub?

Back

B(t) represents the depth of the water in inches, t minutes after Tyler began to fill the bathtub.

Front

Explain the meaning of B(1) < B(7).

Back

The depth of the water at 1 minute was less than the depth of the water at 7 minutes.

Front

What does f(-2) = -9 indicate about the function f?

Back

It indicates that when the input (x) is -2, the output (f(-2)) is -9.

Front

Using a graph, how do you determine the value of f(8)?

Back

You find the point on the graph where x = 8 and read the corresponding y-value.

Front

If a question asks you to find f(2), what does that mean?

Back

It means to evaluate the function f at x = 2.

Front

What is the value of f(2) if it is given as 5?

Back

The output of the function f when the input is 2 is 5.

Front

What is the significance of function notation in mathematics?

Back

Function notation provides a way to express relationships between variables, allowing for easier manipulation and evaluation.

Front

How can you interpret the output of a function?

Back

The output of a function represents the value of the dependent variable based on the input value of the independent variable.

Front

What does it mean if a function is increasing on an interval?

Back

It means that as the input values increase, the output values also increase.

Front

What does it mean if a function is decreasing on an interval?

Back

It means that as the input values increase, the output values decrease.