y=3x/x^2 + 81
for the given equation, list the intercepts and test for symmetry.
You have posted many times, and by now you should know that you will NEED brackets for equations like this to establish the proper order of operation.
I am sure you meant to type:
y = 3x/(x^2 + 81)
when x = 0, y = 0/81 = 0, so the origin is both a y and x intercept
subbing in a positive x will yield a positive y
subbing in a negative x will yield a negative y
but the absolute value will be the same
also , notice that f(-x) = -f(x)
e.g. x = 1, then y = 3/82
if x = -1 , y = -3/81
so there is a reflection in the origin.
The height h(t), in feet, of an airborne tee shirt t seconds after being launched can be approximated by h(t) = - 15t^2+10, 0-<t-<. Find the times when the tee shirt will reach a fan 190 feet above ground level. The tee shirt will reach the fan at how many seconds?
To find the intercepts of the equation y = (3x)/(x^2 + 81), we need to determine the values of x and y when the equation intersects the x-axis and the y-axis.
1. X-intercept(s):
An x-intercept occurs when y = 0. To find the x-intercept(s), set y = 0 in the equation and solve for x:
0 = (3x)/(x^2 + 81)
Multiplying both sides by (x^2 + 81), we get:
0 = 3x
Therefore, the x-intercept(s) is/are x = 0.
2. Y-intercept:
A y-intercept occurs when x = 0. To find the y-intercept, substitute x = 0 into the equation:
y = (3*0)/(0^2 + 81)
y = 0/81
y = 0
Therefore, the y-intercept is y = 0.
Now let's test for symmetry:
To test for symmetry, we need to check the equation for both x-axis symmetry (y-axis reflection) and y-axis symmetry (x-axis reflection).
1. X-axis symmetry (y-axis reflection):
If the equation is the same when we substitute -x for x, then it has x-axis symmetry.
Substituting -x for x in the equation, we get:
y = (3*(-x))/((-x)^2 + 81)
y = (-3x)/(x^2 + 81)
Comparing this with the original equation, y = (3x)/(x^2 + 81), we can see that they are NOT the same. Therefore, the equation does NOT have x-axis symmetry.
2. Y-axis symmetry (x-axis reflection):
If the equation is the same when we substitute -y for y, then it has y-axis symmetry.
Substituting -y for y in the equation, we get:
-y = (3x)/(x^2 + 81)
Multiplying both sides by -1, we get:
y = (-3x)/(x^2 + 81)
Comparing this with the original equation, y = (3x)/(x^2 + 81), we can see that they are the same. Therefore, the equation has y-axis symmetry.
In conclusion, the intercepts of the equation are:
- X-intercepts: x = 0
- Y-intercept: y = 0
And the equation has y-axis symmetry.