The graph of y = f(x) is as shown in the following figure.

Find the following values
(i)` f(-3)" "(ii) f(-2)" "(iii) f(0)`
(iv)` f(2)" "(v) f(3)" "(vi) lim_(x to -3) f(x)`
(vii)` lim_(x to 0) f(x)" "(viii)lim_(x to 2) f(x)" "(ix) lim_(x to 3) f(x)`
`(x) lim_(x to 2^(-)) f(x)" "(xi)lim_(x to -2^(+)) f (x)" "(x ii)lim_(x to 0^(-)) f(x)`
(x iii) `lim_(x to 0^(+)) f(x)`

Explanation

(i) f(-3) does not exist `" "(ii) f(-2) = 1`
(iii)` f(0) =- 1" "(iv) f(2) = 1.5`
(v) ` f(3) =- 1.5" "(vi) underset(x to -3)"lim" f(x) = 0 = 0`
(vii)` underset(x to 0)"lim" f(x)"does not exist as "underset(x to -0^(-))"lim" f(x) =- 2 and underset(x to - 0^(+))"lim" f(x) =- 1`
(viii) `underset(x to 2)"lim" f(x)" does not exist as "underset( x to 2^(-))"lim" f(x) = 0.5 and underset(x to 2^(+))"lim" f(x) =- 2`
(i x) ` underset(x to 3)"lim" f(x) =- 1" "(x) underset(x to -2^(-))"lim" f(x) =- infty`
(x i)` underset(x to -2^(+))"lim" f(x) = infty" "(x ii) underset(x to -0^(-))" lim" f(x) =- 2`
(x iii)` underset(x to - 0^(+))"lim" f(x) =- 1`