Question: Use the graph to determine a. the function's domain; b. the function's range; c. the x-intercepts, if any; d. the y-intercept, if any; and e. the missing function value, indicated by the question mark below.
f(16) = ?
a. The domain of the function is ____. (Type your answer in interval notation.)
Graph: top-right; a blue increasing curve on the coordinate grid starts at the filled point (0, 1) and continues rightward with an arrow to about (20, 5.5), so the function appears defined for x from 0 upward and rises from y = 1 to about y = 5.5.User: range, missing function value
1. **State the problem:** We need to find the domain, range, x-intercepts, y-intercept, and the missing function value $f(16)$ from the given graph.
2. **Domain:** The graph starts at $x=0$ and continues rightward indefinitely. So the domain is all $x$ values from $0$ to infinity.
$$\text{Domain} = [0, \infty)$$
3. **Range:** The graph starts at $y=1$ when $x=0$ and increases to about $y=5.5$ near $x=20$. Since the graph is increasing and continuous, the range is from $1$ to approximately $5.5$.
$$\text{Range} = [1, 5.5]$$
4. **X-intercepts:** The graph does not cross or touch the $x$-axis (no points where $y=0$). So, there are no $x$-intercepts.
$$\text{X-intercepts} = \varnothing$$
5. **Y-intercept:** The graph passes through the point $(0,1)$, so the $y$-intercept is $1$.
$$\text{Y-intercept} = 1$$
6. **Missing function value $f(16)$:** Since the graph is increasing smoothly from $y=1$ at $x=0$ to about $y=5.5$ at $x=20$, we estimate $f(16)$ by interpolating the value on the curve near $x=16$. The graph suggests $f(16)$ is approximately $4.8$.
**Final answers:**
- Domain: $[0, \infty)$
- Range: $[1, 5.5]$
- X-intercepts: None
- Y-intercept: $1$
- $f(16) \approx 4.8$