identify the horizontal asymptote of each graph.\n$t(x)=6^{x}$\n$y = 0$\n$y = 1$\n$y = 6$\ncomplete\n$t(x)=5^…

Explanation:

Step1: Recall exponential - function properties

For an exponential function of the form $y = a\cdot b^{x}+k$ ($b> 0,b\neq1$), when $|x|\to\infty$, if $|b| > 1$, as $x\to-\infty$, $b^{x}\to0$. For the function $t(x)=6^{x}$, as $x\to-\infty$, $6^{x}\to0$. So the horizontal asymptote is $y = 0$. For the function $t(x)=5^{x}-3$, as $x\to-\infty$, $5^{x}\to0$. Then $y=5^{x}-3\to - 3$.

Answer:

For $t(x)=6^{x}$, the horizontal asymptote is $y = 0$. For $t(x)=5^{x}-3$, the horizontal asymptote is $y=-3$.