From the image, we can see that the question is asking to determine the domain and range of a given function, which is displayed as a graph. You have already entered a domain, $[1, 6]$, but the response indicates that it might not be fully correct.

Let's analyze the function visually:

Domain:

The domain of a function represents the set of all possible $x$-values for which the function is defined. From the graph:

• The function starts at $x = 0$ (because the leftmost point seems to be on $x = 0$).
• The function extends until $x = 6$ (the rightmost point on the graph).

Thus, the domain is $[0, 6]$, which includes all $x$-values from 0 to 6.

Range:

The range of a function represents the set of all possible $y$-values the function attains.

• The lowest point of the graph appears to be around $y = 0$.
• The highest point seems to be around $y = 4$.

So, the range of the function is $[0, 4]$, covering all $y$-values from 0 to 4.

Correct answers:

• Domain: $[0, 6]$
• Range: $[0, 4]$

Would you like further details or have any additional questions about this?

Related Questions:

1. What happens to the domain if the graph has a vertical asymptote?
2. How would the range change if there was a discontinuity in the graph?
3. Can you determine the domain of a function if given only an equation, not a graph?
4. How would you write the domain and range if the graph had open endpoints?
5. What types of functions have an infinite domain or range?

Tip:

For graphical problems, always pay close attention to whether the graph includes the endpoints or not, as this can affect whether the interval is open or closed.