Answer:
Domain as an inequality: [tex]\boldsymbol{\text{x} < 6 \ \text{ or } \ -\infty < \text{x} < 6}[/tex]
Domain in interval notation: [tex]\boldsymbol{(-\infty, 6)}[/tex]
Range as an inequality: [tex]\boldsymbol{\text{y} \le 6 \ \text{ or } \ -\infty < \text{y} \le 6}[/tex]
Range in interval notation: [tex]\boldsymbol{(-\infty, 6]}[/tex]
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Explanation:
The domain is the set of allowed x inputs. For this graph, the right-most point is when x = 6. This endpoint is not part of the domain due to the open hole. The graph goes forever to the left to indicate [tex]\text{x} < 6[/tex] but I think [tex]-\infty < \text{x} < 6[/tex] is far more descriptive.
The second format directly leads to the interval notation of [tex](-\infty, 6)[/tex]
Always use parenthesis for either infinity. We use a parenthesis for the 6 to tell the reader not to include it as part of the domain.
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The range is the set of possible y outputs.
The highest y can get is y = 6
Therefore, y = 6 or y < 6
The range can be described as [tex]\text{y} \le 6 \ \text{ or } \ -\infty < \text{y} \le 6[/tex] where the second format is better suited to lead directly to the interval notation [tex](-\infty, 6][/tex]
Use a square bracket to include the 6 as part of the range. We don't have any open holes at the peak mountain point.
