Not all graphing involves lines, although lines play an important role in graphs (as either axes or asymptotes or reflection structures). You can quickly graph circles if you know the center and radius. A parabola has a unique U or cup shape. And once you have the basic shape of a particular graph, you can quickly create variations on that graph by using a few transformational rules.
Here are the graphing techniques you'll use in this chapter:
Keeping all the graphing rules and tips in mind can be tricky; here are a few things to specifically watch out for in this chapter:
966−973 Find the intersection of the lines by graphing.
966.
967.
968.
969.
970.
971.
972.
973.
974−979 Sketch a graph of each circle, indicating the center and the radius.
974. x2 + y2 = 4
975.
976. (x − 2)2 + (y + 1)2 = 9
977. (x + 1)2 + y2 = 16
978. (x − 4)2 + (y − 4)2 = 1
979. x2 + (y − 2)2 = 25
980−989 Sketch the graph of the parabola y = a(x − h)2 + k
980. Vertex: (−1, −2); passes through (0, 0)
981. Vertex: (3, 4); passes through (1, 1)
982. Vertex: (0, 2); passes through (1, 0)
983. Vertex: (3, −1); passes through (−1, 3)
984. y = (x − 3)2 + 1
985. y = (x + 1)2 − 2
986. y = 6 − (x − 2)2
987. y = −1 − (x + 1)2
988. y − 3 = (x + 3)2
989. y + 2 = (x + 4)2
990−1001 Perform the indicated transformation when graphing a new graph from a basic graph.
990. Using the basic graph for y = |x|, sketch the graph of y = |x|+3.
991. Using the basic graph for y = |x|, sketch the graph of y = |x| − 1.
992. Using the basic graph for y = |x|, sketch the graph of y = |x − 2|.
993. Using the basic graph for y = |x|, sketch the graph of y = −|x + 4|.
994. Using the basic graph for y = x3, sketch the graph of y = x3 + 2.
995. Using the basic graph for y = x3, sketch the graph of y = −x3 − 1.
996. Using the basic graph for y = x3, sketch the graph of y = (x − 4)3.
997. Using the basic graph for y = x3, sketch the graph of y = −(x + 1)3.
998. Using the basic graph for y = (x − 1)2, sketch the graph of y = −(x − 1)2 + 1.
999. Using the basic graph for y = (x − 1)2 the graph of y = 2(x − 1)2 − 4.
1000. Using the basic graph for y = (x + 3)2, sketch the graph of y = −(x + 3)2.
1001. Using the basic graph for y = (x + 3)2, sketch the graph of y = −3(x + 3)2 − 2.