The graph models the speed of a car over a function of time during a 3-hour trip. How far did the car go over the course of the
trip?
There is a nice way to visualize this quantity in terms of the graph. If you find it, it will help you solve this problem.
The car traveled a total of ____
miles.
There is a nice way to visualize this quantity in terms of the graph. If you find it, it will help you solve this problem.
The car traveled a total of ____
miles.
1 answer:
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Answer:
• zero: -4, -4/3, 7
• positive: -4 < x < -4/3 . . . or 7 < x
• negative: x < -4 . . . or -4/3 < x < 7
Step-by-step explanation:
Zeros of the function are at x=-4, -4/3, +7. These are the values that make each of the individual factors be zero. For example, x-7=0 when x=7.
The function will be negative for x-values left of an odd number of zeros. It will be positive for x-values left of an even number of zeros (including left of no zeros, which is to say right of all zeros). This is because the sign of the factor giving rise to the zero changes for x-values on either side of that zero. (This is not true for zeros with even multiplicity, as the sign does not change at those.)
