Question

which functions have graphs that are symmetrical with respect to the y-axis
A)odd
B)Both odd & even
c)neither
D) even

Answer 1

@Callisto any idea?

Answer 2

@Calcmathlete

Answer 3

even

Answer 4

The only function which is both even and odd is the constant function which is identically zero (i.e., f(x) = 0 for all x).
The sum of an even and odd function is neither even nor odd, unless one of the functions is equal to zero over the given domain.
The sum of two even functions is even, and any constant multiple of an even function is even.
The sum of two odd functions is odd, and any constant multiple of an odd function is odd.
The product of two even functions is an even function.
The product of two odd functions is an even function.
The product of an even function and an odd function is an odd function.
The quotient of two even functions is an even function.
The quotient of two odd functions is an even function.
The quotient of an even function and an odd function is an odd function.
The derivative of an even function is odd.
The derivative of an odd function is even.
The composition of two even functions is even, and the composition of two odd functions is odd.
The composition of an even function and an odd function is even.
The composition of any function with an even function is even (but not vice versa).
The integral of an odd function from −A to +A is zero (where A is finite, and the function has no vertical asymptotes between −A and A).
The integral of an even function from −A to +A is twice the integral from 0 to +A (where A is finite, and the function has no vertical asymptotes between −A and A).

Answer 5

Yes ana even is correct

Answer 6

wow
i think it is even

Answer 7

For odd function, f(-x)=-f(x) => rotational symmetry
For even function, f(-x) = f(x) => graphs are symmetrical with respect to the y-axis

Answer 8

@Callisto *rotational symmetry about the origin

Answer 9

even means \(f(-x)=f(x)\) and so for example if \((-2,4)\) is on the graph, so is \((2,4)\)

Answer 10

think for example of \(y=x^2\) a nice parabola symmetric with respect to the y axis, and clearly even

Answer 11

@eyust707 Thanks for correcting.

Answer 12

np =P