Transformation of pdf to calculate cdf

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A random variable $X$ has a pdf given by

$$\displaystyle f(x) = \frac{2(x+2)}{25}, -2 < x <3$$

Let $Y=X^2$ be a transformation of $X$.

$1$. Is this transformation one-to-one? Find the support of $Y$.

$2$. Derive the cdf of $Y$.