Graphs of Functions

Front

What is a function in mathematics?

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 F(3) = -6 indicate about the function F?

Back

It indicates that when the input to the function F is 3, the output is -6.

Front

How do you find the value of a function at a specific point, such as F(-8)?

Back

To find the value of a function at a specific point, substitute the input value into the function's equation and solve for the output.

Front

What is the significance of the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the domain of F(x) if it is given as -10 ≤ x ≤ 8?

Back

The domain of F(x) is the interval from -10 to 8, inclusive.

Front

What does F(x) = 2 mean in terms of finding x?

Back

F(x) = 2 means you need to find the value(s) of x for which the output of the function F equals 2.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What is the range of F(x) if it is given as -7 ≤ y ≤ 2?

Back

The range of F(x) is the interval from -7 to 2, inclusive.

Front

How can you determine if a function is increasing or decreasing?

Back

A function is increasing if the output values rise as the input values increase, and decreasing if the output values fall as the input values increase.

Front

What is the difference between a closed interval and an open interval in the context of domain and range?

Back

A closed interval includes its endpoints (e.g., [a, b]), while an open interval does not include its endpoints (e.g., (a, b)).