Radical Function Graphs
A free College Algebra lesson from the “Rational Exponents and Radicals” unit, with a worked example and practice problems including step-by-step solutions.
Square-root functions begin where the radicand is zero and extend in the direction where the radicand is nonnegative. Transformations move the starting point.
What you'll learn
- Interpret square-root graphs
- Find domain restrictions
- Use transformations of radical functions
Worked example
Problem. For y = sqrt(x - 4), what is the smallest x-value in the domain?
- The radicand must be nonnegative.
- x - 4 >= 0.
- x >= 4.
Answer: 4
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. For y = sqrt(x + 2), what is the smallest x-value in the domain?
Show solution
- x + 2 >= 0.
Answer: -2
2. The graph of y = sqrt(x) starts at...
Choices: (0, 0) · (1, 0) · (0, 1) · (-1, 0)
Show solution
- The parent square-root graph starts at the origin.
Answer: (0, 0)
3. For y = sqrt(x - 7) + 3, what is the starting x-value?
Show solution
- The x-shift controls the domain endpoint.
Answer: 7
4. The graph of y = sqrt(x - 5) starts at...
Choices: (5, 0) · (-5, 0) · (0, 5) · (0, -5)
Show solution
- Set x - 5 = 0.
Answer: (5, 0)
5. For y = sqrt(x) + 4, what is the starting y-value?
Show solution
- The parent graph starts at y = 0, then shifts up 4.
Answer: 4
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