Question

of exponential functions
h.

t(x) = 5^x - 3

y = 0
y = -3
y = -5
done

Explanation:

Step1: Recall Asymptote of Exponential

The parent function \( y = a^x \) (here \( a = 5 \)) has a horizontal asymptote at \( y = 0 \). For a transformed function \( t(x)=5^x - 3 \), we apply vertical shift.

Step2: Determine Shifted Asymptote

A vertical shift of \( -3 \) (subtracting 3) moves the asymptote of \( y = 5^x \) (which is \( y = 0 \)) down by 3 units. So the asymptote becomes \( y = 0 - 3=-3 \). Also, observing the graph, the left - hand side of the curve approaches \( y=-3 \) as \( x\to-\infty \).

Answer:

\( y = - 3 \)