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.

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98

answer: the answer is e

step-by-step explanation: