Clear answer | Algebra homework help

 

part1

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  1. Find the vertex of the parabola f(x) = x2 – 16x + 63.
  2. Find the x- and y-intercepts of the cubic function f(x) = (x+4)(2x-1)(x-1).
  3. If f(x) = x2-2x-24 and g(x) = x2-x-30, find (f-g)(x).
  4. If f(x) = x+4 and g(x) = 2×2-x-1, evaluate the composition (g o f)(2).
  5. If f(x) = x+4 and g(x) = 2×2-x-1, find the composition (f o g)(x).
  6. Write the following sentence as an equation: y varies directly as x.
  7. Write the following sentence as an equation: x is directly proportional to y and is inversely proportional to the cube of z.
  8. What are the zeros of the parabola: f(x) = x2 – 7x + 10 (that is, what are the x-intercepts or the points where the graph crosses the x-axis)?
  9. What is the vertical asymptote of the rational function f(x) = 3x / (2x – 1)?
  10. What is the horizontal asymptote of the rational function f(x) = 3x / (2x – 1)?

PART2:

  1. If f(x) = 8x + 16, then find f -1(x).
  2. Determine if the following functions are inverses of each other:
    f(x) = 7x + 14
    g(x) = (1/7)x – 2
  3. Write the exponential equation y = 5x in logarithmic form.
  4. Write the logarithmic equation log7x = y in exponential form.
  5. Use the change-of-base formula to convert x=log390 to common logarithms. Then use a calculator to round the value of x to the nearest thousandth.
  6. Find the amount of money accumulated if you invest $10,000 at 3% interest compounded quarterly for 2 years. Round your answer to the nearest cent.
  7. Find the amount of money accumulated if you invest $10,000 at 3% interest compounded continuously for 2 years. Round your answer to the nearest cent.
  8. Solve the following exponential equation:
    5x = 2
    Round your solution to the nearest hundredth.
  9. Solve the following exponential equation:
    ex = 10
    Round your solution to the nearest hundredth.
  10. Solve the following logarithmic equation:
    log7x + log7(3x-2) = 0
    Be sure to check all of your solutions in the original equation.

part3:

  1. Solve the following equation for n:
    n/4 – 5/6 = 5/12
  2. Solve the following equation for x:
    2x/3 – 4x/5 = 1/15
  3. Solve the following equation for x:
    9/(4x) + 1/3 = 5/(2x)
  4. Solve the following equation for x:
    |5x-7| = 14
    Hint: This absolute value equation will turn into 2 linear equations, so there will be two solutions!
  5. Solve the following system of linear equations: 2x + 3y = -5

-2x + y = 9

6. Solve for (x, y, z), if there is a solution to the given system of linear equations:

– x + 2y + 3z = 0

3x – 2y – 2z = 5

4x + y – 3z = -9

7. Solve: x2 – 4x + 5 = 0.

8, Add the complex numbers: (5 – 2i) + (1 + 6i)

9. Subtract the complex numbers: (4+3i) – (6+i).

10. Multiply the complex numbers (4+3i) (6+i)

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