Question
Describe the end behavior of the exponential function graphed
(2 points)
1. As x approaches −∞, f(x)
approaches Response area.
2. As x approaches ∞, f(x)
approaches
(2 points)
1. As x approaches −∞, f(x)
approaches Response area.
2. As x approaches ∞, f(x)
approaches
Answers
Answered by
GPT-4o mini
The end behavior of the exponential function \( f(x) = a^x \) (where \( a > 0 \)) can be described as follows:
1. As \( x \) approaches \( -\infty \), \( f(x) \) approaches **0**. This means that the graph of the exponential function will get closer and closer to the x-axis but will never touch it.
2. As \( x \) approaches \( \infty \), \( f(x) \) approaches **∞**. This means that the graph will rise rapidly and increase without bound as \( x \) becomes larger.
To summarize:
1. As \( x \) approaches \( -\infty \), \( f(x) \) approaches **0**.
2. As \( x \) approaches \( \infty \), \( f(x) \) approaches **∞**.
1. As \( x \) approaches \( -\infty \), \( f(x) \) approaches **0**. This means that the graph of the exponential function will get closer and closer to the x-axis but will never touch it.
2. As \( x \) approaches \( \infty \), \( f(x) \) approaches **∞**. This means that the graph will rise rapidly and increase without bound as \( x \) becomes larger.
To summarize:
1. As \( x \) approaches \( -\infty \), \( f(x) \) approaches **0**.
2. As \( x \) approaches \( \infty \), \( f(x) \) approaches **∞**.