Question

If y2 = x3 + 2, which statement is true?


A. The equation is a function at all values of x.
B. The equation is not a function.
C. The equation is a function only when x < 0
D. The equation is a function only when x > 0.

Answer 1

A) is a function at all values of x.

Answer 2

hint:
our function exixts if and only if:
\[x + 2 \geqslant 0\]

Answer 3

exists*

Answer 4

more precisely the expression:
\[\sqrt {{x^3} + 2} \]
exists if:
\[x + 2 \geqslant 0\]

Answer 5

we have to keep in mind that we have two branches, namely:
\[y = \sqrt {{x^3} + 2} \]
and
\[y = - \sqrt {{x^3} + 2} \]

Answer 6

oops..I have made an error, since the two branches esist if
\[x + \sqrt[3]{2} \geqslant 0\]

Answer 7

we have this graph, approximatively

now please make the vertical line test