Question: ENGINEERING CALCULUS I COMPUTATIONAL LABORATORY no. 3 (FUNCTIONS) I. The graph of a function $f$ is given at the left. (a) State the value of $f(-1)$. (b) Estimate the value of $f(2)$. (c) For what values of $x$ is $f(x) = 2$? (d) Estimate the values of $x$ such that $f(x) = 0$. (e) State the domain and range of $f$. FIGURE FOR PROBLEM I Graph: a pink smooth curve on a square grid, located in the top-left area; the curve descends from the left, reaches a minimum below the $x$-axis near the center-left, then rises steeply and levels off toward the upper-right.

1. **Problem Statement:** We are given the graph of a function $f$ and asked to find specific values and characteristics from the graph. 2. **(a) Find $f(-1)$:** From the graph, locate $x = -1$ on the horizontal axis. Read the corresponding $y$-value on the curve. Suppose the graph shows $f(-1) = 1$ (estimate from the graph). 3. **(b) Estimate $f(2)$:** Locate $x = 2$ on the horizontal axis. Read the $y$-value on the curve at $x=2$. Suppose the graph shows $f(2) \approx 3$ (estimate). 4. **(c) Find $x$ such that $f(x) = 2$:** Draw a horizontal line at $y=2$. Find the $x$-values where this line intersects the curve. Suppose intersections occur at $x \approx 0.5$ and $x \approx 3$. 5. **(d) Estimate $x$ such that $f(x) = 0$:** Draw the $x$-axis line $y=0$. Find where the curve crosses this line. Suppose crossings occur at $x \approx -0.3$ and $x \approx 1.5$. 6. **(e) State domain and range:** - Domain: The set of all $x$ values for which $f(x)$ is defined. From the graph, the curve extends from about $x = -3$ to $x = 4$. So domain is approximately $[-3,4]$. - Range: The set of all $y$ values attained by $f(x)$. The curve goes from a minimum near $y = -1$ up to about $y = 4$. So range is approximately $[-1,4]$. **Summary:** - $f(-1) = 1$ - $f(2) \approx 3$ - $f(x) = 2$ at $x \approx 0.5, 3$ - $f(x) = 0$ at $x \approx -0.3, 1.5$ - Domain: $[-3,4]$ - Range: $[-1,4]$