Question

ying asymptotes of exponential functions
identify the horizontal asymptote of the graph.
$y = -3$
$y = 0$
$y = -5$
graph: a coordinate plane with a curve labeled $t(x) = 5^x - 3$

Explanation:

Step1: Recall exponential function asymptote

For an exponential function of the form \( f(x)=a^{x}+k \) (where \( a>0,a
eq1 \)), the horizontal asymptote is \( y = k \).

Step2: Identify the function and k

The given function is \( t(x)=5^{x}-3 \). Here, comparing with \( f(x)=a^{x}+k \), we have \( a = 5 \) and \( k=-3 \).

Step3: Determine the horizontal asymptote

Using the rule for the horizontal asymptote of exponential functions, the horizontal asymptote of \( t(x)=5^{x}-3 \) is \( y=-3 \).

Answer:

\( y = -3 \) (corresponding to the option \( y=-3 \))