Using Function's Graph
There is a picture of a function's graph with a curve CONNECTING the following points on the xy-plane:
(-6, 3), (-3, 0), (0, 3), (2, 4), (6, 0), (8, -2), (10, 0)
and (11, 1).
QUESTIONS: a - d.
(a) Is f(8) positive or negative? Why? Why not?
(b) For what numbers x is f(x) > 0?
(c) What are the x-and y-intercepts, IF ANY?
(d) How often does the line y = 1/2 intersect the graph?
Originally Posted by symmetry
a.) f(8) is asking what the y value is at x = 8; we are given (8, -2), so at x = 8, y = -2. From this information, do you think f(8) is positive or negative? It should be self explanatory. In fact, on the interval from x = -6 to x = 11, the only time the graph is negative is between x = 6 and x = 10.
b.) Nice, I practically answered this answer in a. Take all the other values and you have when f(x) > 0.
c.) This question is asking when is x = 0 and when is y = 0. Just by looking at the graph and seeing when the graph goes through the x and y-axis, you should be able to answer this question. Or, just look at the points, and see when the x or y values are 0.
d.) y = 1/2 is a horizontal line. Draw a horizontal line at y = 1/2.
It will intersect the graph exactly 4 times.
It's easier than I thought.