The given function is even.
Solution:
If f(-x) = f(x), then the function is even.
If f(-x) = -f(x), then the function is odd.
Given function:
[tex]f(x)=x^{6}-x^{4}[/tex]
Substitute x = -x
[tex]f(-x)=(-x)^{6}-(-x)^{4}[/tex]
[tex]=x^{6}-x^{4}[/tex]
= f(x) (given)
f(-x) = f(x)
From the definition, it is even.
Hence the given function is even.
Given f(x) and g(x) = k·f(x), use the graph to determine the value of k.
g(x)
The diagram for this exercise is attached below. We have two linear functions [tex]f(x) \ and \ g(x)[/tex] and the following relationship:
[tex]g(x) = kf(x)[/tex]
From the graph, we know that:
[tex]f(-3)=1 \\ \\ g(-3)=-3[/tex]
Then, substituting into the relationship:
[tex]g(-3)=kf(-3) \\ \\ -3=k(1) \\ \\ \\ Finally: \\ \\ \boxed{k=-3}[/tex]