Question

In any function, f(x) = a(x-h)n + k , a negative leading coefficient means the graph is reflected. True or False

Answer 1

Answer:

True

Step-by-step explanation:

For any function of the form $f(x) = a(x-h) ^ n + k$ the coefficient a produces a reflection of the function whenever $a$.

We can verify it in the following way.

Take, for example, the function:

$f(x) = 2(x-1) ^ 3$

Now let's make $f(2)$

$f(2) = 2(2-1)^3\\\\f(2) = 2$

Now let's $f(2)$ in the following function:

$f(x) = -2(x-1)^3$

We have:

$f(2) = -2(2-1)^3\\\\f(2) = -2$

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.