13Show work and no Cursive writing Parts a and bGet it right for a thumbs up **Finding Limits using a Graph**In this exercise, you are asked to determine the limits of a function \( f(x) \) using its graph. Let's go through the steps to find the limit for specific values of \( x \).### Limits to Find1. \( \lim\limits_{x \to 3} f(x) \)2. \( \lim\limits_{x \to -1} f(x) \)### Steps:1. Locate \( x = 3 \) and \( x = -1 \) on the graph of the function \( f(x) \).2. Determine the corresponding \( y \)-values (function values) as \( x \) approaches 3 and -1.3. If the function approaches a single finite value as \( x \) gets close to 3 and -1, that value is the limit. 4. If the \( y \)-value doesn't settle on a single number (i.e., if it keeps oscillating or there is a discontinuity), then the limit does not exist.### Questions:#### a. Find \( \lim\limits_{x \to 3} f(x) \) or state if it doesn't exist.Select the correct choice below and fill in any answer boxes in your choice.- **A.** \( \lim\limits_{x \to 3} f(x) = \_\_\_\_ \) (Type an integer.)- **B.** The limit does not exist.#### b. Find \( \lim\limits_{x \to -1} f(x) \) or state if it doesn't exist.Select the correct choice below and fill in any answer boxes in your choice.- **A.** \( \lim\limits_{x \to -1} f(x) = \_\_\_\_ \) (Type an integer.)- **B.** The limit does not exist.### Explanation of the Task:To complete the exercise, you need to analyze the provided graph and identify whether \( f(x) \) approaches a specific value as \( x \) gets infinitely close to the given values (3 and -1). Your selection should reflect whether the limit exists and if it does, you should provide the correct integer for the limit. **Graph Description for Educational Website**This image showcases a two-dimensional graph plotted on a Cartesian coordinate system. The x-axis and y-axis are labeled, and the graph displays a smooth, continuous curve with various peaks and troughs. Below is a detailed explanation of the graph's elements:1. **Axes and Grid Lines** - **X-Axis**: The horizontal axis, denoted by \( x \), ranges from -4 to 4. - **Y-Axis**: The vertical axis, denoted by \( y \), ranges from -4 to 4. - The grid lines facilitate easier reading and plotting of values.2. **Curve Characteristics** - The purple curve originates from the far-left, descending from 4 on the y-axis. - The curve then ascends, peaking slightly above the y=4 line, before descending again to touch the x-axis at approximately x=-3. - Following this, the curve dips below the x-axis, reaching a local minimum around y=-3 at x=-2. - After this low point, the curve ascends again to cross the x-axis at around x=0 before it reaches another peak at x=1 and y=2. - The curve finally descends, crossing the x-axis once more around x=1.5 and ending at x=2 and y=-2.3. **Special Points** - **Intersections**: The curve crosses the x-axis at roughly x=-3, x=0, and x=1.5. - **Extremes**: The graph shows two peaks (maximums) and two troughs (minimums). - Peak 1: Around (x=-3.5, y=4.5) - Peak 2: (x=1, y=2) - Trough 1: (x=-2, y=-3) - Trough 2: (x=2, y=-2)4. **Arrows** - The arrows at the ends of the curve on the left and right sides indicate that the function continues beyond the plotted range.Overall, the graph represents a polynomial function with multiple turns and indicates the function's general shape, illustrating a combination of increasing and decreasing intervals. This type of graph is often used in algebra and calculus to study the behavior of polynomial functions.

Answered: Image /qna-images/answer/af949c4b-db38-4e35-94a6-6e45d85a6017.jpg

Use the graph to find the following limits. a. lim f(x) b. lim f(x) X-3 X→-1 a. Find lim f(x) or state that it doesn't exist. Select the correct choice below and fill in any answer boxes in your choice. X-3 A. lim f(x) = x - 3 (Type an integer.) OB. The limit does not exist. b. Find lim f(x) or state that it doesn't exist. Select the correct choice below and fill in any answer boxes in your choice. X→-1 O A. (... lim f(x) = X-1 (Type an integer.) OB. The limit does not exist.