Does the following graph represent a function or a relation?

Does the following graph pass the vertical or horizontal line test?

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

Find the following values:
(i) `underset(x to 4 )"lim" f(x)" "(ii) underset(x to - 3)"lim "f(x)`
` (iii) underset(x to 0^(+))"lim "f(x)" "(iv) underset(x to 0^(-))"lim " f(x)`
`(v) underset(x to 0)"lim "f(x)" "(vi) f(-2)`
`(vii) underset(x to 2^(-))"lim "f(x)" "(viii) underset(x to -2^(-))"lim "f(x)`
`(ix) underset(x to 0)"lim "f(x+1)" "(x) f(0)`
` (x i) underset(x to 0^(+))"lim "f(x-2)" "(x ii) underset(x to 1^(-))"lim " f(x-4)`

For the function g whose graph is given. Arrange the following numbers in increasing order and explain your reasoning.
`g(0), g'(-2), g'(0), g'(2), g'(4)`

The graph of a function is shown in the following figure.

Determine the intervals on which the function is concave up and the intervals on which it is concave down. Find the x - coordinates of any inflection points.

The graph of f(x) is given. State with reasons the number at which the function is non-differentiable.

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

(i) Find the sum of the roots of the equation f (x) = 0.
(ii) Find the product of the roots of the equation f(x) = 4.
(iii) Find the absolute value of the difference of the roots of the equation f(x) = x+2 .

Does the following graph pass the vertical or horizontal line test ?

Following is the graph of y = f' (x) , given that f(c) = 0. Analyse the graph and answer the following questions.
(a) How many times the graph of y = f(x) will intersect the x - axis?
(b) Discuss the type of roots of the equation f (x) = 0, ` a le x le b`.
(c) How many points of inflection the graph of ` y = f(x), a le x le b`, has?
(d) Find the points of local maxima/minima of` y = f(x), a lt x b`.
(e) How many roots equation ` f''(x) = 0` has?

The graph of functions are given in the following fingure. Discuss the symmetry.