For the given equation, list the intercepts and test for symmetry.
2+y-121=0
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If you mean 2x+y-121=0 there's no symmetry.
If you mean x^2+y-121=0 then
y=121-x^2
symmetry about the line x=0
I assume you can find the intercepts.
To find the intercepts of the equation, we need to determine where the equation crosses the x-axis and the y-axis.
To find the x-intercept, we set y = 0 and solve for x:
2 + y - 121 = 0
2 + 0 - 121 = 0
-119 = 0
From this, we see that there is no x-intercept because -119 does not equal 0.
To find the y-intercept, we set x = 0 and solve for y:
2 + y - 121 = 0
2 + y - 121 = 0
y = 119
Therefore, the y-intercept is at the point (0, 119).
Now let's test for symmetry. There are two types of symmetry we commonly encounter:
1. X-axis symmetry (also known as y-axis reflection symmetry): If a function is symmetric about the x-axis, its graph is identical when reflected across the x-axis. To test for x-axis symmetry, we replace y with -y in the equation and simplify:
2 + (-y) - 121 = 0
2 - y - 121 = 0
If the resulting equation is equivalent to the original equation, then the graph is symmetric with respect to the x-axis. Here, the resulting equation is different from the original equation, so the graph is not symmetric about the x-axis.
2. Y-axis symmetry (also known as x-axis reflection symmetry): If a function is symmetric about the y-axis, its graph is identical when reflected across the y-axis. To test for y-axis symmetry, we replace x with -x in the equation and simplify:
2 + y - 121 = 0
2 + y - 121 = 0
Since the resulting equation is the same as the original equation, the graph is symmetric with respect to the y-axis.
In this case, the equation is symmetric about the y-axis but not about the x-axis.