Answer:
True
Step-by-step explanation:
For any function of the form [tex]f(x) = a(x-h) ^ n + k[/tex] the coefficient a produces a reflection of the function whenever [tex]a <0[/tex].
We can verify it in the following way.
Take, for example, the function:
[tex]f(x) = 2(x-1) ^ 3[/tex]
Now let's make [tex]f(2)[/tex]
[tex]f(2) = 2(2-1)^3\\\\f(2) = 2[/tex]
Now let's [tex]f(2)[/tex] in the following function:
[tex]f(x) = -2(x-1)^3[/tex]
We have:
[tex]f(2) = -2(2-1)^3\\\\f(2) = -2[/tex]
We can see then that the function was reflected in the axis -y by placing a negative coefficient a.
You can see more examples in the attached images
Therefore we can conclude that the statement is true.
