To determine which statement is not a key feature of the function $h(x)$, let's analyze the given information and each statement:

Given Function Definition:

1. $h(x) = x^2 - 5$ when $0 \leq x \leq 3$
2. $h(x) = -\log_3(x)$ when $x > 3$

Analysis of the Statements:

1. Domain of $h(x)$:

   • The first part $x^2 - 5$ is defined for $0 \leq x \leq 3$.
   • The second part $-\log_3(x)$ is defined for $x > 3$.
   • Combining these, the domain of $h(x)$ is $[0, \infty)$.
   • This statement is correct.

2. Range of $h(x)$:

   • For $x^2 - 5$, when $0 \leq x \leq 3$, the output ranges from $-5$ (at $x = 0$) to $4$ (at $x = 3$).
   • For $-\log_3(x)$, when $x > 3$, the function will produce negative values decreasing without bound as $x$ increases.
   • Thus, the range of $h(x)$ is $(-\infty, 4]$.
   • This contradicts the statement that the range is $(-\infty, \infty)$. This statement is incorrect.

3. The y-intercept of $h(x)$:

   • The y-intercept occurs when $x = 0$. Here, $h(0) = 0^2 - 5 = -5$.
   • The y-intercept is indeed $(0, -5)$.
   • This statement is correct.

4. End behavior of $h(x)$ as $x \to \infty$:

   • As $x \to \infty$, $h(x) = -\log_3(x)$ and $\log(x)$ grows unbounded, so $-\log_3(x)$ approaches $-\infty$.
   • This statement is correct.

Conclusion:

The incorrect statement is that the range of $h(x)$ is $(-\infty, \infty)$. The correct range is $(-\infty, 4]$.

Summary:

The feature that is NOT true about the function $h(x)$ is:

The range of $h(x)$ is $(-\infty, \infty)$.

Would you like more details or have any questions? Here are five related questions:

1. How do you determine the range of a piecewise function?
2. What is the importance of identifying the domain and range in functions?
3. Can logarithmic functions have a range of $(-\infty, \infty)$?
4. How does end behavior influence the analysis of functions?
5. Why is it important to verify each feature of a function when analyzing it?

Tip: Always graph a function if possible, as it helps visually confirm the domain, range, intercepts, and end behavior.