Exercises: Describe Qualitatively the Functional Relationship Between Two Quantities by Analyzing a Graph

Decreasing — the output gets smaller as the input gets larger.

Constant — the output stays the same as the input gets larger.

Increasing — the output gets larger as the input gets larger.

The rate of change is constant — it changes by the same amount for each equal step.

The rate of change is speeding up as you move right, since the line keeps climbing.

The rate of change is slowing down as you move right, since a line eventually flattens.

The starting value — where the function begins, since graphs are usually read starting from their highest point.

The maximum — the largest output value the function reaches.

The rate of change at that point, since a high point is where the graph is steepest.

The temperature is decreasing the whole time, but it stays positive (above the axis).

The temperature becomes negative because the graph goes down, and down always eventually crosses zero.

The temperature is increasing because the line is moving to the right as time passes.

Two: it goes up and then comes down.

Three: it increases, then stays constant, then decreases.

One: the whole graph is a single function.

Nonlinear, and it is still a function — every input has exactly one output.

Nonlinear, so it is not a function — only straight lines are functions.

Linear, because it is one smooth piece with no breaks or corners in it.

Yes — a steeper section always means the object is moving faster.

No — a steep section means the car has stopped.

No — on a speed graph, a steep section means the speed is changing quickly (fast acceleration), not that the speed is highest.

At the bottom of the dip in the middle, where the curve turns from falling to rising.

At the left end, where the graph starts, since that is usually the smallest input value shown.

At the right end, where the graph ends, since that is usually the smallest output value shown.