Questions and Answers
What is the simplified form of $(81x^6)^{1/2}$?
9x^3
What is the simplified form of $(16x^{16})^{1/4}$?
2x^4
Simplify the expression $(3 rac{1}{4} + 3 rac{3}{4})^{-2}$.
1/9
Simplify the expression $(2 rac{8}{5} + 2 rac{7}{5})^{-2}$.
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What is the range of $f(x) = |x + 2| - 3$?
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What is the domain of $|{ rac{3}{x + 4}}| - 7$?
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Which function represents a translation of 5 down and 7 left?
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Which function $g(x)$ represents a translation of 11 units to the right and 8 units up from the parent function $f(x) = ext{√}x$?
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Given $|{ rac{3}{x - 4}}| + 3 = -2$, what is the value of x?
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Given $|{ rac{3}{x + 6}}| + 3 = 7$, what is the value of x?
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Study Notes
Simplification of Expressions
- The simplified form of ((81x^6)^{1/2}) is (9x^3).
- The simplified form of ((16x^{16})^{1/4}) is (2x^4).
- The expression ((3 \frac{1}{4} + 3 \frac{3}{4})^{-2}) simplifies to (\frac{1}{9}).
- The expression ((2 \frac{8}{5} + 2 \frac{7}{5})^{-2}) simplifies to (\frac{1}{64}).
Function Range and Domain
- The range of the function (f(x) = |x + 2| - 3) is ({-3, \infty}).
- The domain of the function (\frac{3}{|x + 4|} - 7) is ((-\infty, \infty)).
Function Translations
- A function that is translated 5 units down and 7 units left is represented as (g(x) = \frac{3}{|x + 7|} - 5).
- A function representing a translation of 11 units to the right and 8 units up from the parent function (f(x) = \sqrt{x}) is (g(x) = \frac{3}{|x - 11|} + 8).
Solving for x
- The equation (\frac{3}{|x - 4|} + 3 = -2) yields the solution (x = -121).
- The equation (\frac{3}{|x + 6|} + 3 = 7) gives the solution (x = 58).
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Prepare for your Algebra 2 exam with this no calculator review quiz. The flashcards cover essential topics such as simplification and function ranges, providing a comprehensive review of key concepts. Test your understanding and readiness for the exam!
