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 transformation called a reflection in the x-axis whenever $a<0$, that is, this axis is said to be a mirror. Let's take an example, suppose you have a function:

$f(x)=4(x-2)^2+5$

If the leading coefficient is now -4, then the graph is reflected and the new function is:

$f(x)=-4(x-2)^2+5$

This is shown in the figure below. The red parabola represents $f(x)=4(x-2)^2+5$ and the blue parabola is $f(x)=-4(x-2)^2+5$. As you can see, the red parabola has been reflected and transformed into the blue one.