Answer all blank 16) **Understanding Continuity and Discontinuity of Functions**The image contains a mathematical exercise focused on analyzing the continuity and discontinuity of a function, \( f(x) \), at a specific point \( x = -1 \). Below is a detailed transcription and explanation that can be used on an educational website.---### Graph AnalysisThe graph displayed is a coordinate plane with \( x \) and \( y \) axes extending to at least -5 and 5 in both directions. The function plotted has noticeable changes or breaks near \( x = -1 \).### Instructions and Exercises1. **Finding Limits and Function Value:** - Find \(\lim_{x \to -1^-} f(x)\): [Input Field] - Find \(\lim_{x \to -1^+} f(x)\): [Input Field] - Find \(\lim_{x \to -1} f(x)\): [Input Field] - Find \( f(-1) \): [Input Field]2. **Determining Continuity:** Determine if the function is continuous or discontinuous at the limit value. If it is discontinuous, indicate if the discontinuity is removable or non-removable. - [ ] The function is continuous at \( x = -1 \) - [ ] The function has a removable discontinuity at \( x = -1 \) - [ ] The function has a non-removable discontinuity at \( x = -1 \)3. **Identifying the Type of Discontinuity:** If the function has a discontinuity at the limit value, check all the boxes that indicate why the function is discontinuous there. - [ ] \( f(-1) \) does not exist - [ ] \(\lim_{x \to -1} f(x)\) does not exist - [ ] \( f(-1) \) and \(\lim_{x \to -1} f(x)\) both exist, but \( f(-1) \neq \lim_{x \to -1} f(x) \)### Explanation**Limit from the Left (\(\lim_{x \to -1^-} f(x)\)):**This represents the limit of the function as \( x \) approaches -1 from the left-hand side.**Limit from the Right (\(\lim_{x \to -1^+} f(x

A function is said to be continuous at if .

-5 -44 43 -2 03 2 H -1 -2 03- Find lim f (x) Find lim f (x) x411+ Find lim f(x) HI-1 2 3 4 Find f(-1) Determine if the function is continuous or discontinuous at the limit value. If it is discontinuous, indicate if the discontinuity is removable or non-removable. O The function is continuous at x = -1 O The function has a removable discontinuity at x = -1 O The function has a non-removable discontinuity at x = -1 If the function has a discontinuity at the limit value, check all the boxes that indicate why the function is discontinuous there. Of(-1) does not exist' Olim f(x) does not exist x-1 Of(-1) and lim f (x) both exist, but f(-1) lim f(x) 24-1