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)?
x
y
Answer
Multiple Choice Answers
as , x, right arrow, infinity, comma, f, left bracket, x, right bracket, right arrow, infinity, and , as , x, right arrow, minus, infinity, comma, f, left bracket, x, right bracket, right arrow, infinityas x→∞,f(x)→∞ and as x→−∞,f(x)→∞
as , x, right arrow, infinity, comma, f, left bracket, x, right bracket, right arrow, minus, infinity, and , as , x, right arrow, minus, infinity, comma, f, left bracket, x, right bracket, right arrow, minus, infinityas x→∞,f(x)→−∞ and as x→−∞,f(x)→−∞
as , x, right arrow, infinity, comma, f, left bracket, x, right bracket, right arrow, infinity, and , as , x, right arrow, minus, infinity, comma, f, left bracket, x, right bracket, right arrow, minus, infinityas x→∞,f(x)→∞ and as x→−∞,f(x)→−∞
as , x, right arrow, infinity, comma, f, left bracket, x, right bracket, right arrow, minus, infinity, and , as , x, right arrow, minus, infinity, comma, f, left bracket, x, right bracket, right arrow, infinityas x→∞,f(x)→−∞ and as x→−∞,f(x)→∞
The correct answer is: as \( x\rightarrow \infty \), \( f(x)\rightarrow \infty \) and as \( x\rightarrow -\infty \), \( f(x)\rightarrow \infty \)
The correct answer is: as x→∞, f(x)→−∞ and as x→−∞, f(x)→−∞.
To determine the end behavior of f(x), we need to analyze the behavior of the function as x approaches positive infinity and as x approaches negative infinity.
As x approaches positive infinity (x → ∞), we can see from the graph that f(x) is increasing without bound. This means that f(x) goes to positive infinity (f(x) → ∞) as x approaches infinity.
As x approaches negative infinity (x → -∞), we can see from the graph that f(x) is also increasing without bound. However, in this case, f(x) approaches negative infinity (f(x) → -∞) as x approaches negative infinity.
So, the correct answer is: as x approaches ∞, f(x) approaches ∞, and as x approaches -∞, f(x) approaches -∞.