Interpreting & Sketching Functions

Front

What is a constant function?

Back

A constant function is a function that does not change its value; it remains the same for all inputs. For example, f(x) = 5 is constant because it always equals 5.

Front

How do you determine the interval where a function is constant?

Back

To determine the interval where a function is constant, look for sections of the graph where the y-value does not change as x changes.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, as x increases, the value of f(x) also increases.

Front

How can you identify the interval where a function is increasing from a graph?

Back

You can identify the interval where a function is increasing by looking for sections of the graph that slope upwards from left to right.

Front

What is the significance of the slope in a distance-time graph?

Back

The slope of a distance-time graph represents speed. A steeper slope indicates a faster speed.

Front

What does a horizontal line represent in a distance-time graph?

Back

A horizontal line in a distance-time graph indicates that the object is at rest; the distance does not change over time.

Front

How do you interpret a graph that shows a person hiking away from a campsite?

Back

The graph will show an increasing distance from the campsite, followed by a flat line during rest, and then a decreasing distance as they return.

Front

What is the formula for calculating cost based on time?

Back

Cost = Rate × Time. For example, if the rate is $9 per hour, then for 2 hours, the cost is $9 × 2 = $18.

Front

What does it mean when a graph has a negative slope?

Back

A negative slope indicates that as x increases, y decreases, which can represent a return trip or a decrease in distance.

Front

How can you tell if a function is decreasing on a graph?

Back

A function is decreasing on a graph if the line slopes downwards from left to right.