The graph of y, equals, f, left bracket, x, right brackety=f(x) is graphed below. What is the end behavior of f, left bracket, x, right bracketf(x)?
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Answer
Multiple Choice Answers
as , x, right arrow, infinity, comma, y, right arrow, infinity, and , as , x, right arrow, minus, infinity, comma, y, right arrow, infinityas x→∞,y→∞ and as x→−∞,y→∞
as , x, right arrow, infinity, comma, y, right arrow, infinity, and , as , x, right arrow, minus, infinity, comma, y, right arrow, minus, infinityas x→∞,y→∞ and as x→−∞,y→−∞
as , x, right arrow, infinity, comma, y, right arrow, minus, infinity, and , as , x, right arrow, minus, infinity, comma, y, right arrow, minus, infinityas x→∞,y→−∞ and as x→−∞,y→−∞
as , x, right arrow, infinity, comma, y, right arrow, minus, infinity, and , as , x, right arrow, minus, infinity, comma, y, right arrow, infinityas x→∞,y→−∞ and as x→−∞,y→∞
The correct answer is: as x→∞,y→∞ and as x→−∞,y→∞
The end behavior of the graph of y = f(x) can be determined by observing the behavior of the graph as x approaches positive infinity and negative infinity.
From the given options, the correct answer is:
- as x approaches positive infinity (x → ∞), y approaches positive infinity (y → ∞)
- as x approaches negative infinity (x → -∞), y also approaches positive infinity (y → ∞)
So the correct choice is:
as x→∞,y→∞ and as x→−∞,y→∞
To determine the end behavior of the function f(x), we need to examine the behavior of y as x approaches positive infinity and as x approaches negative infinity.
To find how y behaves as x approaches positive infinity, observe the right-hand side of the graph. Does y increase or decrease without bound as x becomes larger? If y increases without bound as x→∞, the end behavior can be described as: as x→∞, y→∞.
Next, we need to determine the behavior as x approaches negative infinity. Examine the left-hand side of the graph. Does y decrease or increase without bound as x becomes more negative? If y increases without bound as x→−∞, the end behavior can be described as: as x→−∞, y→∞.
Therefore, the correct answer is: as x→∞, y→∞ and as x→−∞, y→∞.