On a seperate sheet of paper, answer questions 1-7 in the first section and the two questions in the second section.

Section 1
There is a direct relation between the rate of change of a function and the slope of its lines.

Study the graph to the left. Carlos and Maria are on their way to school. On a seperate piece of paper, answer the following questions using interval notation. (For example, (A,B) would represent all values of t between A and B.)

1. For what values of time (t) are Carlos and Maria stopped?
2. For what values of t do they increase their speed?
3. Which of these increase at the same rate?
4. How does increasing or decreasing speed correspond to the slope of the line in the graph?
5. For what values of t do Carlos and Maria decrease their speed?
6. At what time (t) do they achieve their highest speed?
7. For what values of t do Carlos and Maria drive at a constant rate?

Section 2

Consider the diagram below. We are familiar with the slope of straight lines. Now, the line y = mx + b can be thought of as a function of x, like f(x) = mx + b, where y = f(x). If a function is decreasing, the line is falling, and the slope is negative. If a function is increasing, the line is rising, and the slope is positive. If a function maintains a constant value, the line is horizontal, and the slope is 0. What about a vertical line? What is the slope of a vertical line? What's your guess about how a function that is a vertical line can be interpreted?

Slippery Slopes

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