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Comprehensive Final Review of Algebra Problems and Solutions

This extensive final review covers multiple algebra concepts, designed to bolster your understanding and problem-solving skills. You will tackle extraneous solutions, logarithmic equations, sequences, and more. The review includes practical problems such as finding domains and ranges, modeling inverse variations, solving equations, and identifying intercepts. Additionally, you'll explore the relationship between different logarithmic functions and composite functions. Perfect for students looking to refine their algebra abilities before exams.

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Comprehensive Final Review of Algebra Problems and Solutions

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  1. Slide the Eraser Final Review

  2. Solve. Check for extraneous solutions. Question #1

  3. Solve. Check for extraneous solutions. Question #2

  4. Solve. Check your solution. Question #3

  5. Use the properties of logarithms to simplify and solve the equation. log 2 + log x = 1 Question #4

  6. Find the 10th term of the following sequence. 25, -5, 1, …. Question #5

  7. State the domain and range of: f(x) = 2x2 - 12x + 5 Question #6

  8. Suppose that y and x vary inversely. Write a function that models the variation and find y when x = 10. x = 2.5 when y = 100 Question #7

  9. Solve the following equation. 52x = 20 Question #8

  10. Divide. State any restrictions on the variables. Question #9

  11. How are y = log8x and y = 8x related? Question #10

  12. Find the x and y-intercepts of: f(x) = x2 + 2x - 15 Question #11

  13. If f(x) = 2x3 and g(x)= 3x + 7 find g(f(x)) Question #12

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