College Algebra, 2013a

42 Relations and Functions
51. 4y 2 − 9x 2 =36
Re-write as: y = ±
√
9x 2 +36
2
.
The graph has no x-intercepts
y-intercepts: (0, ±3)
x y (x, y)
−4 ±3 √ 5 ( −4, ±3 √ 5 )
−2 ±3 √ 2 ( −2, ±3 √ 2 )
0 ±3 (0, ±3)
2 ±3 √ ( √ )
2 2, ±3 2
4 ±3 √ ( √ )
5 4, ±3 5
7
6
5
4
3
2
1
−4−3−2−1 1 2 3 4
−1
−2
−3
−4
−5
−6
−7
y
x
52. x 3 y = −4
Re-write as: y = − 4 x 3 .
The graph has no x-intercepts
The graph has no y-intercepts
x y (x, y)
−2
1
2
(−2, 1 2 )
−1 4 (−1, 4)
− 1 2
32 (− 1 2 , 32)
1
2
−32 ( 1 2 , −32)
1 −4 (1, −4)
2 − 1 2
(2, − 1 2 )
y
32
4
x
−2 −1 1 2
−4
The graph is symmetric about the x-axis
The graph is symmetric about the y-axis
The graph is symmetric about the origin
−32
The graph is not symmetric about the
x-axis (e.g. (1, −4) is on the graph but
(1, 4) is not)
The graph is not symmetric about the
y-axis (e.g. (1, −4) is on the graph but
(−1, −4) is not)
The graph is symmetric about the origin