What is the end behavior of the graph of f(x) = -0.25x2 - 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.
Please help! I have no idea!
To determine the end behavior of the graph of the function f(x) = -0.25x^2 - 2x + 1, we need to look at the leading term of the equation, which is -0.25x^2.
Since the leading coefficient is negative (-0.25), the graph of the function will open downward. This means that as x approaches positive infinity (∞), f(x) will approach negative infinity (-∞), and as x approaches negative infinity (-∞), f(x) will also approach negative infinity (-∞).
Therefore, the correct answer is option D) As x increases, f(x) decreases. As x decreases, f(x) increases.
To determine the end behavior of a graph, we examine what happens to the graph as x approaches positive and negative infinity.
For the given function f(x) = -0.25x^2 - 2x + 1, we observe that it is a quadratic function with a leading coefficient of -0.25.
A quadratic function with a negative leading coefficient (-0.25 in this case) has an inverted U-shaped graph called a downward-opening parabola. The negative leading coefficient indicates that the parabola is concave down.
As x approaches positive infinity, the parabola's arms will point downward without bound since the negative leading coefficient means the graph is decreasing. Therefore, the graph of f(x) will decrease without bound as x increases.
Similarly, as x approaches negative infinity, the parabola's arms will also point downward without bound. The graph will decrease without bound as x decreases.
From this analysis, we can conclude that as x increases, f(x) decreases, and as x decreases, f(x) decreases.
Therefore, the correct answer is B) As x increases, f(x) decreases. As x decreases, f(x) decreases.