identify the horizontal asymptote of each graph.\n$t(x)=6^{x}$\n$y = 0$\n$y = 1$\n$y = 6$\ndone
identify the horizontal asymptote of each graph.\n$t(x)=6^{x}$\n$y = 0$\n$y = 1$\n$y = 6$\ndone
Answer
Explanation:
Step1: Recall exponential - function property
For an exponential function of the form (y = a\cdot b^{x}+k) ((a\neq0), (b>0), (b\neq1)), when (a > 0) and (b>1) (in (t(x)=6^{x}), (a = 1), (b = 6), (k = 0)), as (x\to-\infty), (y\to0).
Step2: Determine the horizontal asymptote
The horizontal asymptote of the exponential function (y = 6^{x}) is the value that (y) approaches as (x\to\pm\infty). Since (6^{x}>0) for all real - valued (x) and (\lim_{x\to-\infty}6^{x}=0), the horizontal asymptote is (y = 0).
Answer:
A. (y = 0)