4.2 Key Features of Graphs

Front

What does it mean for a graph to be decreasing?

Back

A graph is decreasing on an interval if the y-values (output) decrease as the x-values (input) increase. For example, if a temperature graph shows a decrease from 4 pm to midnight, it indicates that the temperature is dropping during that time.

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. For example, if a temperature function has a range from 95 to 116 degrees, it means the temperature can vary between these two values.

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. For example, if a function is defined for the time interval from 0 to 24 hours, this is its domain.

Front

What does absolute minimum mean in the context of a graph?

Back

The absolute minimum is the lowest point on the graph, representing the smallest output value of the function. For example, if the lowest temperature recorded is 95 degrees, this is the absolute minimum.

Front

What does absolute maximum mean in the context of a graph?

Back

The absolute maximum is the highest point on the graph, representing the largest output value of the function. For example, if the highest temperature recorded is 116 degrees, this is the absolute maximum.

Front

How do you identify intervals of increase on a graph?

Back

Intervals of increase can be identified by observing where the graph rises as you move from left to right. If the y-values increase as the x-values increase, that interval is increasing.

Front

How do you identify intervals of decrease on a graph?

Back

Intervals of decrease can be identified by observing where the graph falls as you move from left to right. If the y-values decrease as the x-values increase, that interval is decreasing.

Front

What is a function?

Back

A function is a relation that assigns exactly one output value for each input value. For example, a temperature function assigns a specific temperature to each hour of the day.

Front

What is a graph?

Back

A graph is a visual representation of data or a function, typically using a coordinate system to show the relationship between two variables.

Front

What does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph. This means you can draw the graph without lifting your pencil.