The image shows the graph of the function $t(x) = 5^x - 3$. The task appears to involve determining the horizontal asymptote of the function from the given choices:

1. $y = 0$
2. $y = -3$
3. $y = -5$.

Solution:

The horizontal asymptote of an exponential function like $t(x) = 5^x - 3$ can be found by analyzing the behavior of the function as $x \to -\infty$. Here's the reasoning:

1. The function $5^x$ becomes very small (approaches $0$) as $x \to -\infty$, because exponential decay dominates.
2. Therefore, $t(x) = 5^x - 3$ will approach $-3$ as $x \to -\infty$.

Thus, the horizontal asymptote is: $y = -3$

Final Answer:

The correct choice is: $y = -3$.

Would you like a detailed explanation of the function's behavior or further examples?
Here are 5 related questions to extend your understanding:

1. What happens to the graph of $t(x) = 5^x - 3$ if the "-3" is replaced by a different constant, such as "+2"?
2. How do you find the horizontal asymptote for a more general exponential function, like $t(x) = a^x + b$?
3. What is the domain and range of $t(x) = 5^x - 3$?
4. How does the base $5$ in $5^x$ affect the shape of the graph compared to $2^x$ or $10^x$?
5. What is the significance of the horizontal asymptote in real-world applications of exponential functions?

Tip: Always remember that the horizontal asymptote of $a^x + b$ is determined by the constant $b$, as $a^x \to 0$ when $x \to -\infty$.