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

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

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

Constant — the output stays the same 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.

The rate of change is slowing down as you move right.

The maximum — the largest output value the function reaches.

The starting value — where the function begins.

The rate of change at that point.

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

The temperature becomes negative because the graph goes down.

The temperature is increasing because the line is moving to the right.

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

Two: it goes up and then comes down.

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.

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

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

No — a steep section means the car has stopped.

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.

At the right end, where the graph ends.