Mathematics

Problem

Let

f(x) = x^{2}

. a. (i) Choose any five non-zero values of

x

and tabulate the corresponding

y

-values. Show that for every chosen

x

, the same

y

occurs at

-x

. b. (ii) Hence, prove that

f(x)

is an even function. c. (iii) Using this property, justify why it is sufficient to plot the graph only for

x \geq 0

and then reflect it to obtain the complete graph. d. (iv) After drawing the full graph, estimate the set of all real numbers

x

for which

y < 3

and express your answer in interval notation.