Consider the function given by

MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

Consider the function

p:[-2,2]\to\mathbb{R}

given by

p(x)=\sqrt{4-x^{2}}+x

. Respond to the questions below. (i) Explain why the domain of

p

is exactly the closed interval

[-2,2]

. (ii) Let

p(x)=y

. Eliminate the square root to obtain a polynomial relation between

x

and

y

. (iii) Taking into account the domain condition from part (i), determine all possible real values of

y

that satisfy the relation obtained in part (ii). (iv) Hence, write the range of

p

in interval notation.