<h2>
Answer:</h2>
f(x) ---- even function.
g(x) ----- odd function
h(x) ----- even function.
<h2>
Step-by-step explanation:</h2>
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.
<u> f(x):</u>
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.
<u> h(x):</u>
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.
<u> g(x):</u>
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.