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, minus, infinity, comma, f, left bracket, x, right bracket, right arrow, minus, infinity, and , as , x, right arrow, infinity, comma, f, left bracket, x, right bracket, right arrow, infinityas x→−∞,f(x)→−∞ and as x→∞,f(x)→∞
as , x, right arrow, minus, infinity, comma, f, left bracket, x, right bracket, right arrow, minus, infinity, and , as , x, right arrow, infinity, comma, f, left bracket, x, right bracket, right arrow, minus, infinityas x→−∞,f(x)→−∞ and as x→∞,f(x)→−∞
as , x, right arrow, minus, infinity, comma, f, left bracket, x, right bracket, right arrow, infinity, and , as , x, right arrow, infinity, comma, f, left bracket, x, right bracket, right arrow, infinityas x→−∞,f(x)→∞ and as x→∞,f(x)→∞
as , x, right arrow, minus, infinity, comma, f, left bracket, x, right bracket, right arrow, infinity, and , as , x, right arrow, infinity, comma, f, left bracket, x, right bracket, right arrow, minus, infinityas x→−∞,f(x)→∞ and as x→∞,f(x)→−∞
as x→−∞,f(x)→−∞ and as x→∞,f(x)→∞
The correct answer is:
As x → -∞, f(x) → -∞ and as x → ∞, f(x) → ∞
To determine the end behavior of the function f(x) based on the given graph, you need to determine what happens to the y-values (f(x)) as x approaches positive infinity (+∞) and negative infinity (-∞).
Start by examining the behavior of f(x) as x approaches positive infinity (+∞). Look at the right-hand side of the graph. If the y-values (f(x)) increase without bound as x moves to the right, then the end behavior is that f(x) approaches positive infinity (+∞) as x approaches positive infinity.
Next, consider the behavior of f(x) as x approaches negative infinity (-∞). Look at the left-hand side of the graph. If the y-values (f(x)) decrease without bound as x moves to the left, then the end behavior is that f(x) approaches negative infinity (-∞) as x approaches negative infinity.
Based on these observations, the correct answer is:
- as x → -∞, f(x) → -∞
- as x → +∞, f(x) → +∞
Therefore, the correct choice is:
as x → -∞, f(x) → -∞, and as x → +∞, f(x) → +∞