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Question

Feature
An exponential function is graphed on the coordinate plane. The graph starts just above y equals 2 and curves up and to the right forever.
Question
Use the graph to answer the question.
Describe the end behavior of the graphed function.
(1 point)
Responses

f left-parenthesis x right-parenthesis right arrow 2 as x right arrow negative infinity and f left-parenthesis x right-parenthesis right arrow infinity as x right arrow infinity
Image with alt text: f left-parenthesis x right-parenthesis right arrow 2 as Image with alt text: x right arrow negative infinity and Image with alt text: f left-parenthesis x right-parenthesis right arrow infinity as Image with alt text: x right arrow infinity

f left-parenthesis x right-parenthesis right arrow negative infinity as x right arrow 2 and f left-parenthesis x right-parenthesis right arrow infinity as x right arrow infinity
Image with alt text: f left-parenthesis x right-parenthesis right arrow negative infinity as Image with alt text: x right arrow 2 and Image with alt text: f left-parenthesis x right-parenthesis right arrow infinity as Image with alt text: x right arrow infinity

f left-parenthesis x right-parenthesis right arrow 2 as x right arrow negative infinity and f left-parenthesis x right-parenthesis right arrow infinity as x right arrow 4
Image with alt text: f left-parenthesis x right-parenthesis right arrow 2 as Image with alt text: x right arrow negative infinity and Image with alt text: f left-parenthesis x right-parenthesis right arrow infinity as Image with alt text: x right arrow 4

f left-parenthesis x right-parenthesis right arrow negative infinity as x right arrow negative infinity and f left-parenthesis x right-parenthesis right arrow infinity as x right arrow infinity

Answer 1

To describe the end behavior of an exponential function that starts just above \( y = 2 \) and curves up and to the right forever, we look at what happens to the function values as \( x \) approaches negative infinity and positive infinity.

1. As \( x \) approaches negative infinity (\( x \to -\infty \)), the function approaches a horizontal asymptote. Since the graph starts just above \( y = 2 \), we can say that: \[ f(x) \to 2 \quad \text{as} \quad x \to -\infty \]

2. As \( x \) approaches positive infinity (\( x \to \infty \)), the function value goes up without bound, which means: \[ f(x) \to \infty \quad \text{as} \quad x \to \infty \]

Based on this analysis, the correct description of the end behavior is: \[ f(x) \to 2 \quad \text{as} \quad x \to -\infty \quad \text{and} \quad f(x) \to \infty \quad \text{as} \quad x \to \infty \]

Thus, the correct response is:

f(x) → 2 as x → -∞ and f(x) → ∞ as x → ∞