The graph of x^3+y^3=4 is symmetric with respect to which of the following?

a.
y-axis
c.
line y = x
b.
x-axis
d.
none of the above

Choice C. The line y =x

Step-by-step explanation:

A function f(x) is symmetric with respect to the y-axis if f(-x) = f(x). If we substitute -x in place of x we end up with a different function. So the function is not symmetric with respect to the y-axis.

Moreover, the function is not symmetric with respect to the x-axis since substituting -y in place of y results into a new function.

If we plot the graph of the function together with the line y =x on the same graph we note that the line y =x acts as a mirror line such that one half of the function lies on the upper end and the other half on the lower end. The function is thus symmetric with respect to the line y =x.

Option C is the correct option.

Step-by-step explanation:

The given graph is in the form of x³+y³ = 4

To check the symmetry of the function about y-axis we put (-x) in place of x in the given function and if we get no change in the function then it is symmetric to y- axis.

(-x)³ + y³ = 4

-x³ + y³ = 4

This function is different from the original one. Therefore non symmetric to the y axis.

Similarly for x axis we put (-y) in place of y the equation becomes as

x³ + (-y)³ = 4

x³ - y³ = 4

Again the given function is non symmetric to x axis

for y = x

by putting x in place of y and y in place of x we get

y³ + x³ = 4

Which exactly same as the original equation. therefore the function is symmetric to the line y = x.

Option C is the correct answer.

  y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x             y

0             0

1             -3

3             -9

-2             6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.

trapezoid

step-by-step explanation:

first i plotted all my points on a grid graph

i made sure all of them were in the correct quadrant

then i saw it was a trapezoid or a quadrilateral