What is the end behavior of the graph of f(x) = -0.25x^2 - 2x + 1?
A) As x increases, f(x) increases. As x decreases, f(x) decreases. ***
B) As x increases, f(x) decreases. As x decreases, f(x) decreases.
C) As x increases, f(x) increases. As x decreases, f(x) increases.
D) As x increases, f(x) decreases. As x decreases, f(x) increases.
I'm not very good at math so if someone could help me
F(x) = -0.25x^2 - 2x + 1.
F(0) = -0.25*0^2 - 2*0 + 1 = 0 + 0 +1 = 1.
F(1) = -0.25*1^2 - 2*1 + 1 = -0.25 - 2 + 1 = -1.25. decreased.
F(2) =
Sure, I can help you with that!
To determine the end behavior of a function, we need to look at its leading term, which is the term with the highest degree. In this case, the leading term is -0.25x^2.
The end behavior of a function is described by what happens to the function as the input (x) approaches positive infinity (increases without bound) and negative infinity (decreases without bound).
When the leading term is negative, like in this case, the graph of the function opens downwards, forming a "U" shape, which is often called a "parabola".
Since the leading coefficient is -0.25, the graph is wider (flatter) than the standard parabola y = x^2. It means that as x approaches positive infinity or negative infinity, the function values (y) will get closer to zero, but never actually reach zero.
So, based on the shape of the parabola and the fact that the leading coefficient is negative, we can conclude that as x increases, f(x) decreases, and as x decreases, f(x) also decreases.
Therefore, the correct answer is option B) As x increases, f(x) decreases. As x decreases, f(x) decreases.