Math  /  Algebra

QuestionGraph the piecewise function f(x)={x if x32x+1 if x>3f(x)=\left\{\begin{array}{r}x \text { if } x \leq-3 \\ -2 x+1 \text { if } x>-3\end{array}\right. and find its domain DD and range RR.

Studdy Solution
The range of a function is the set of all possible y-values. For the first piece of the function, f(x)=xf(x) = x for x3x \leq -3, the y-values are also less than or equal to -3. For the second piece of the function, f(x)=2x+1f(x) = -2x +1 for x>3x > -3, the y-values are greater than -5. So the range is R=(,5)[3,)R = (-\infty, -5) \cup [-3, \infty).

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