I'm unable to view or analyze images directly. However, if you can describe the graphs or provide details about the functions shown in the image, I’d be happy to help you determine their
domains and ranges.
For now, here’s a general guide on how to find
domain and range from a graph:
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🔍 Domain:
The set of all possible
x-values (horizontal extent) for which the function is defined.
- Look at the
leftmost and
rightmost points on the graph.
- If the graph extends infinitely in either direction, use infinity symbols: $(-\infty, \infty)$.
- If there are breaks or holes, exclude those x-values.
---
📈 Range:
The set of all possible
y-values (vertical extent) that the function produces.
- Look at the
lowest and
highest points on the graph.
- Again, consider whether it's bounded or unbounded.
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✔ Common Examples:
1.
Linear Function (straight line):
- Domain: $(-\infty, \infty)$
- Range: $(-\infty, \infty)$
2.
Parabola opening upward (vertex at bottom):
- Domain: $(-\infty, \infty)$
- Range: $[k, \infty)$ where $k$ is the y-coordinate of the vertex.
3.
Square root function:
- Domain: $[a, \infty)$ where $a$ is the starting x-value.
- Range: $[0, \infty)$
4.
Absolute value function:
- Domain: $(-\infty, \infty)$
- Range: $[0, \infty)$
5.
Circle:
- Domain: $[a - r, a + r]$ (horizontal span)
- Range: $[b - r, b + r]$ (vertical span)
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Please describe the graphs in your image — for example:
- Are they lines, parabolas, circles, absolute value, etc.?
- Do they have endpoints, arrows (indicating continuation), or breaks?
Once I know that, I can help you determine the domain and range for each!
Parent Tip: Review the logic above to help your child master the concept of domain and range of graphs worksheet.
