Posted by Hannah on Wednesday, October 6, 2010 at 7:55pm.
Sorry I wanted to add something else!
Determine whether the graph of the following equation is symmetric with respect to the x-axis, the y-axis, and the origin.
y^2 - x - 49 = 0
For x axis -y^2 - x - 9 = 0 is not the same as the first equation so it is not symmetrical to the x-axis. Correct?
For the y-axis y^2 + x - 49 = 0 is not the same as the first equation so it is not symmetrical to the y-axis. Correct?
For the origin -y^2 + x - 49 = 0 is not the same as the first equation so itis not symmetrical to the origin either. Am I correct?
a. (f + g)(x) = f(x) + g(x) =(2x - 3 +
2x^2.
b. (f - g)(x) = f(x) - g(x) = (2x -3)
- 2x^2.
c. (f * g)(x) = f(x) * g(x) = (2x -3)
* 2x^2 = 4x^3 - 6x^2.
y^2 - x - 49 = 0.
Solve for x:
x = y^2 - 49 = 0,
This x parabola is the difference of 2 squares:
(y + 7) (y - 7) = 0,
y + 7 = 0,
y = -7,
y - 7 = 0,
y = 7.
Axis of symmetry: y = (-7+7)/2 = 0,
y = 0 is a hor line which lies on the x axis.
c. (f.g)(2) = f(2) * g(2) = (2*2-3) *
(2 * 2^2) = 1 * 8 = 8.
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