Question
Find the domain and range of $f(x)=|2 x-3|-3$.
✓
Answer
Given, $\mathrm{f}(\mathrm{x})=|2 \mathrm{x}-3|-3$
The domain of the expression is all real number except where the expression is undefined. In this case, there is not real number that makes the expression undefined.
$\therefore$ Domain of $\mathrm{f}=(-\infty, \infty)=\mathrm{R}$
The absolute value of expression has a 'V' shape. The range of a positive absolute value expression starts at its vertex and extends to infinity.
Range of $\mathrm{f}=[-3, \infty)$ or $\{y: y \geq-3\}$
The domain of the expression is all real number except where the expression is undefined. In this case, there is not real number that makes the expression undefined.
$\therefore$ Domain of $\mathrm{f}=(-\infty, \infty)=\mathrm{R}$
The absolute value of expression has a 'V' shape. The range of a positive absolute value expression starts at its vertex and extends to infinity.
Range of $\mathrm{f}=[-3, \infty)$ or $\{y: y \geq-3\}$
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