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

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

The end behavior of the described exponential function can be summarized as follows:

• As \( x \) approaches negative infinity, \( f(x) \) approaches 2 (it approaches but does not reach 2, suggesting a horizontal asymptote).
• As \( x \) approaches positive infinity, \( f(x) \) approaches infinity.

Thus, the correct response would be:

f(x) → 2 as \( x \) → -∞ and f(x) → ∞ as \( x \) → +∞.