Use the graph of the function \( I \) shown to the right to estimate the indicated function valuos and limits. Complete parts ( \( A \) ) through ( \( E \) ). B. The limit does not exist. (B) Find the value of \( \lim _{x \rightarrow-3^{\circ}} 1(x) \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( \lim _{x \rightarrow-3^{+}} f(x)=3 \) B. The limit does not exist. (C) Find the value of \( \lim _{x \rightarrow-3} l(x) \). Select the correct choice below and, if necessary, till in the answer box to complete your choice A. The limit does not exist. (D) Find the function value \( f(-3) \). Select the correct choice beluw and, if necessary, fill in the answer box to complete your choice. A. \( f(-3)=\square \) B. The value does not exist.

To accurately determine the limits and function values for the function \( f(x) \) at \( x = -3 \), it's essential to reference the provided graph of \( f(x) \). Since I don't have access to the graph, I'll guide you through the general process of how to approach each part based on typical scenarios involving limits and function values. ### **Part (B): Find \( \lim_{x \rightarrow -3^{+}} f(x) \)** **Options:** - **A.** \( \lim_{x \rightarrow -3^{+}} f(x) = 3 \) - **B.** The limit does not exist. **Approach:** - **Right-Hand Limit (\( -3^{+} \)):** Examine the behavior of \( f(x) \) as \( x \) approaches -3 from values greater than -3 (to the right on the number line). - **If** the function approaches a specific value (e.g., 3), then **Option A** is correct. - **If** the function approaches different values from the right or exhibits unbounded behavior, then **Option B** is correct. **Example Scenarios:** - If the graph approaches the point \( (-3, 3) \) from the right, then **Option A** is correct. - If there's a jump, oscillation, or vertical asymptote as \( x \) approaches -3 from the right, then **Option B** is correct. ### **Part (C): Find \( \lim_{x \rightarrow -3} f(x) \)** **Options:** - **A.** The limit does not exist. **Approach:** - **Two-Sided Limit:** Determine the behavior of \( f(x) \) as \( x \) approaches -3 from both the left (\( -3^{-} \)) and the right (\( -3^{+} \)). - **If** both one-sided limits exist and are equal, the two-sided limit exists and equals that common value. - **If** the one-sided limits are unequal or at least one does not exist, then the two-sided limit does not exist. **Example Scenarios:** - If \( \lim_{x \rightarrow -3^{-}} f(x) = 2 \) and \( \lim_{x \rightarrow -3^{+}} f(x) = 3 \), then **Option A** ("The limit does not exist.") is correct. - If both one-sided limits are equal (e.g., both approach 3), then the two-sided limit exists and equals that value. ### **Part (D): Find \( f(-3) \)** **Options:** - **A.** \( f(-3) = \square \) (Specify the value based on the graph) - **B.** The value does not exist. **Approach:** - **Function Value at a Point:** Look at the graph to see if there's a closed circle (filled dot) at \( x = -3 \). - **If** there's a defined point, note its y-value and select **Option A**, filling in the blank with that value. - **If** there's an open circle or no point at \( x = -3 \), then **Option B** is correct, indicating that \( f(-3) \) is not defined. **Example Scenarios:** - If the graph shows a point at \( (-3, 3) \), then **Option A** with \( f(-3) = 3 \) is correct. - If the graph has a hole or an asymptote at \( x = -3 \), then **Option B** ("The value does not exist.") is correct. ### **General Tips:** 1. **Identify the Type of Discontinuity:** - **Removable Discontinuity:** If the limit exists but the function value is either not defined or different from the limit, there's a "hole" in the graph. - **Jump Discontinuity:** If the left and right limits exist but are not equal, the two-sided limit does not exist. - **Infinite Discontinuity:** If the function grows without bound as it approaches the point, the limit does not exist. 2. **Consistent Notation:** - Ensure that superscripts (like \( ^{+} \) or \( ^{-} \)) are correctly placed to indicate the direction from which \( x \) approaches the point. 3. **Refer to the Graph Carefully:** - Pay attention to open vs. closed circles, the direction of approaching arrows, and any asymptotic behavior near the point of interest. If you can provide specific details or describe the graph near \( x = -3 \), I can offer more precise assistance!