Part B
Choose all of the following statements that describe the graph.
A.
As x approaches negative infinity, f(x) approaches 0.
B. As x approaches negative infinity, f(x) approaches infinity
C. As x approaches infinity, f(x) approaches 0.
D. As x approaches infinity, f(x) approaches infinity.
Please solve as fast as you can

[tex] \displaystyle \large{ \lim_{x \to \infty} {a}^{x} = \infty \: \: \: (a > 1)} \\ \displaystyle \large{ \lim_{x \to \infty} {a}^{x} = 1 \: \: \: (a = 1)} \\ \displaystyle \large{ \lim_{x \to \infty} {a}^{x} = 0 \: \: \: ( |a| < 1)} \\ \displaystyle \large{ \lim_{x \to \infty} {a}^{x} = no \: \: \: limit \: \: \: (a \leqslant - 1)} \\[/tex]

Limit at negative infinity

[tex] \displaystyle \large{ \lim_{x \to - \infty} {a}^{x} = 0 \: \: \: (a > 1)} \\ \displaystyle \large{ \lim_{x \to - \infty} {a}^{x} = 1 \: \: \: (a = 1)} \\ \displaystyle \large{ \lim_{x \to - \infty} {a}^{x} = \infty \: \: \: ( |a| < 1)} \\ \displaystyle \large{ \lim_{x \to - \infty} {a}^{x} = no \: \: \: limit \: \: \: (a \leqslant - 1)} \\[/tex]

Derived from Infinite Geometric Sequence.

For a>1, when x approaches infinite, y approaches infinite too.

For a=1, when x approaches infinite, y approaches 1.

For |a| < 1 or 0 < a < 1, when x approaches infinite, y approaches 0.

For a ≤ -1, when x approaches infinite, y approaches both infinity and negative infinity but since lim + ≠ lim - then it does not exist.

However, the explanation above is limit which is calculus so it may be advanced.

From the graph, x keeps increasing then y keeps increasing too and when x keeps decreasing, y keeps decreasing almost to 0.