Question

Label each function as even, odd, or neither.

Answer 1

an even function has symmetry about the x axis

this means that if you fold the graph over the y axis, the function will map over itself

in number terms, if f(x) is an even function, then f(x)=f(-x)

an example is f(x)=x²

an odd function has symmetry about the origin

it is kinda confusing, but if g(x) is an odd function, g(-x)=-g(x)

an example is g(x)=x³

the first one (f(x)) seems to be neither

h(x) one, notice for x=2 and -2, the values are negative of each other, this tells us that it's an odd function

g(x), replacing x with -x gives us -|-2x|+3=-|2x|+3, same function, even function

Answer 2

Answer:

            f(x)  ---- even function.

            g(x) -----  odd function

            h(x)  -----  even function.

Step-by-step explanation:

We know that a function f(x) is:

            even if:  f(-x)=f(x)                

and        odd if:   f(-x)= -f(x)

Also, if none of the above property hold true that it is neither even nor odd.

Also , from a graph we have that the graph of a even function have both the ends in the same direction. and also it has a symmetry along a line parallel to the y-axis.

                                     f(x):

Hence, from the given figure of function f(x) we see that the graph of a function is symmetric about a line x=4.

              Hence, function f(x) is a even function.

                                          h(x):

We are given a set of values for function h(x) as:

 x          -2   -1   0     1     2

h(x)        8    4   0   -4    -8

Hence, we see that:

h(-2)= -h(2)

h(-1) = -h(1)

h(-0)= -h(0)

Hence we could say from these values that h(-x)= -h(x)

Hence, the function h(x) is a odd function.

                                            g(x):

g(x)= -|2x|+3

Also,

g(-x)=-|-2x|+3

g(-x)= -|2x|+3

g(-x) = g(x)

As g(-x)=g(x)

Hence, the function g(x) is a even function.