Question

identify the horizontal asymptote of each graph.
t(x) = 6^x
options: y = 0; y = 1; y = 6

Explanation:

Step1: Recall Exponential Asymptote

For an exponential function \( t(x) = a^x \) (where \( a > 0, a
eq 1 \)), the horizontal asymptote is \( y = 0 \) (since as \( x \to -\infty \), \( a^x \to 0 \)).

Step2: Analyze \( t(x) = 6^x \)

The function \( t(x) = 6^x \) is an exponential function with \( a = 6 \). As \( x \) approaches negative infinity, \( 6^x \) approaches 0. Visually, the graph of \( t(x) = 6^x \) (seen in the provided plot) approaches the x - axis (where \( y = 0 \)) as \( x \) becomes very small (negative direction).

Answer:

\( y = 0 \)