Question

graph of t(x) = 5^x - 3. options: y=0, y=-3, y=-5

Explanation:

Step1: Recall Asymptote of Exponential Function

The parent function of \( t(x) = 5^x - 3 \) is \( f(x)=5^x \). The horizontal asymptote of \( y = a^x \) (where \( a>0,a
eq1 \)) is \( y = 0 \).

Step2: Analyze Vertical Shift

For the function \( t(x)=5^x - 3 \), it is a vertical shift of the parent function \( f(x) = 5^x \) down by 3 units. When we shift a function \( y = f(x) \) vertically by \( k \) units (downward if \( k>0 \)), the horizontal asymptote of \( y=f(x)-k \) is \( y=-k \). Here, \( k = 3 \), so the horizontal asymptote of \( t(x)=5^x - 3 \) is \( y=-3 \).

Answer:

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