Determine whether the graph of each function is symmetric with respect to the y-axis or the origin.?

Question

f(x)=15/x

Answer 1

is symmetric if the figures are the same!

Answer 2

The function f(x) = 15/x is the same as 15 * 1/x, where 15 is the slope of the line, and 1/x is the shape of the line.

The function f(x) = 1/x is the reciprocal function.
For positive values of x, then 1/x gets smaller and smaller as x grows larger. If x=1, then f(x) = 1; x=2, f(x) = 0.5; x=10, f(x) = 0.1; x=100, f(x) = 0.01, etc.
For negative values of x, then 1/x gets also smaller in value as x grows more negative. The same values as above, only negative for both x and 1/x.

Note the special point of 0. When x approaches 0 (either a small positive or negative number), then f(x) approaches infintity, because 1/0 = infinity. For example, when x = 0.5, f(x) = 2; x=0.1, f(x) = 10; x=0.001, f(x) = 1000, etc.

On a sheet of graph paper, plot the values as above and draw the line f(x), and see what happens to the shape of f(x) for all values of x and -x.
If you can see the same shape of f(x) for both +x and -x values around the y axis, then f(x) is symmetric.

Answer 3

The way to determine if it is symmetric:

If it is symmetric about the Y axis, then f(-X) is equal to f(x).

If it is symmetric about the origin, then f(-X) is equal to -f(x).

Plug -x in for x. 15/-x = -f(X) It is therefore symmetric about the origin.

Hope this helps!

Sue

Answer 4

Your section is all angles from 0 stages to 360 stages - the 4 quadrants. in case you obtain 40 8.6 stages as one answer, this is contained interior the 1st quadrant. sin (40 8.6 stages) = sin (131.4 stages) First quadrant and 2d quadrant