Characteristics of Functions - IM2

Front

What is a function?

Back

A function is a relation that assigns exactly one output value for each input value.

Front

What is 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 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 does it mean for a function to have a maximum value?

Back

A function has a maximum value at a point where the function reaches its highest output compared to nearby points.

Front

What does it mean for a function to have a minimum value?

Back

A function has a minimum value at a point where the function reaches its lowest output compared to nearby points.

Front

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

Back

A function is increasing on an interval if the output values rise as the input values increase; it is decreasing if the output values fall as the input values increase.

Front

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

Back

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

Front

How can you express the range of a function in inequality notation?

Back

The range can be expressed in inequality notation by indicating the minimum and maximum output values, such as a ≤ y ≤ b.

Front

What is the notation for the domain of a function?

Back

The domain can be expressed using set notation, such as D = {x | condition}, or by listing the specific values.

Front

What is the difference between discrete and continuous functions?

Back

Discrete functions have distinct, separate values, while continuous functions have an unbroken range of values.