$$ 1 \leftarrow $$ The function $$ f $$ is defined as follows. Complete parts (a) to (d) below. $$ f(x)=\left\{\begin{array}{ll}x+6 & ext { if }-4 \leq x1\end{array} ight. $$ (a) Find the domain of the function. The domain of the function $$ f $$ is (Type your answer in interval notation.)

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$$ 1 \leftarrow $$ The function $$ f $$ is defined as follows. Complete parts (a) to (d) below. $$ f(x)=\left\{\begin{array}{ll}x+6 & 	ext { if }-4 \leq x<1 \ 8 & 	ext { if } x=1 \ -x+3 & 	ext { if } x>1\end{array}ight. $$ (a) Find the domain of the function. The domain of the function $$ f $$ is (Type your answer in interval notation.)

UpStudy AI · Accepted Answer

1. The function $$ f $$ is defined by three pieces:
   - For $$-4 \leq x < 1$$, $$ f(x) = x + 6 $$.
   - For $$x = 1$$, $$ f(x) = 8 $$.
   - For $$x > 1$$, $$ f(x) = -x + 3 $$.

2. We must determine all $$ x $$-values for which $$ f(x) $$ is defined.  
   - The first piece covers $$ x $$ in the interval $$[-4, 1)$$.
   - The second piece covers $$ x = 1 $$.
   - The third piece covers $$ x $$ in the interval $$(1, \infty)$$.

3. Combining these intervals, the function $$ f $$ is defined for every $$ x $$ in the interval from $$-4$$ to $$\infty$$.

4. In interval notation, the domain of $$ f $$ is  
   $$
   [-4, \infty)
   $$
The domain of the function $$ f $$ is $$[-4, \infty)$$.

The function is defined as follows. Complete parts (a) to (d) below.

(a) Find the domain of the function.
The domain of the function is
(Type your answer in interval notation.)

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The function is defined as follows. Complete parts (a) to (d) below. (a) Find the domain of the function. The domain of the function is (Type your answer in interval notation.)