If $$ f(x) $$ is defined as follows, find (a) $$ f(-3) $$, (b) $$ f(0) $$, and (c) $$ f(3) $$ $$ f(x)=\left\{\begin{array}{ll}x^{2} & ext { if } x0\end{array} ight. $$ (a) $$ f(-3)=\square $$ (Simplify your answer.)

Question

If $$ f(x) $$ is defined as follows, find (a) $$ f(-3) $$, (b) $$ f(0) $$, and (c) $$ f(3) $$ $$ f(x)=\left\{\begin{array}{ll}x^{2} & 	ext { if } x<0 \ -2 & 	ext { if } x=0 \ 2 x+2 & 	ext { if } x>0\end{array}ight. $$ (a) $$ f(-3)=\square $$ (Simplify your answer.)

UpStudy AI · Accepted Answer

1. Since $$ f(x) $$ is defined piecewise, we first identify which piece applies when $$ x = -3 $$.

2. For $$ x < 0 $$, the function is defined as:
   $$
   f(x) = x^2
   $$
   Since $$-3 < 0$$, we use this definition.

3. Substitute $$ x = -3 $$ into the formula:
   $$
   f(-3) = (-3)^2
   $$

4. Calculate:
   $$
   (-3)^2 = 9
   $$

Thus, the answer for part (a) is:
$$
f(-3) = 9
$$
$$ f(-3) = 9 $$

If \( f(x) \) is defined as follows, find (a) \( f(-3) \), (b) \( f(0) \), and (c) \( f(3) \) \( f(x)=\left\{\begin{array}{ll}x^{2} & \text { if } x<0 \\ -2 & \text { if } x=0 \\ 2 x+2 & \text { if } x>0\end{array}\right. \) (a) \( f(-3)=\square \) (Simplify your answer.)

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