Algebra 2 ACP Exam Review

General Instructions

• Use a TI3 calculator (available in Google Classroom) on a split screen while watching the video.
• Pause the video to attempt solving questions before checking the solutions.

Key Topics and Steps

1. Finding Inverses of Functions

• Example: f(x) = log base 2 of x + 4 - 8
• Steps:
  1. Switch x and y: x = log base 2 of y + 4 - 8
  2. Isolate the log expression: x + 8 = log base 2 of y + 4
  3. Change forms: Convert the log equation to an exponential form.
  4. Isolate y: y = 2^(x+8) - 4

2. Graphing Inverses with Domain Restrictions

• Example: f(x) = (x - 3)^2 + 5
• Steps:
  1. Find the inverse by switching x and y.
  2. Solve for y step-by-step.
  3. Choose the appropriate branch for the graph based on domain restrictions.

3. Solving Square Root Equations

• Steps:
  1. Move terms outside the root to isolate the square root expression.
  2. Square both sides to eliminate the square root.
  3. Solve the resulting polynomial equation.

4. Transformations

• Understanding Transformations:
  • Vertical shifts: plus/minus outside shifts up/down.
  • Horizontal shifts: plus/minus inside are opposite (left/right).
  • Vertical compression/stretch: depends on the number coefficient (<1 for compression, >1 for stretch).
  • Reflections over axes: determined by negative signs in function.

5. Converting Between Exponential and Logarithmic Forms

• Steps:
  1. Recognize the base and exponent.
  2. Use the properties of logs: ln for natural logs with base e.

6. Solving Logarithmic Equations

• Steps:
  1. Combine logs using properties into one.
  2. Change the log equation to exponential form.
  3. Solve the resulting equation, possibly using a calculator.

7. Solving Rational Exponent Equations

• Steps:
  1. Isolate the term with the exponent.
  2. Use reciprocal of the exponent to eliminate it.
  3. Solve for the variable.

8. Simplifying Radicals

• Steps:
  1. Create factor trees to simplify terms under the square root.
  2. Pair up factors to bring them outside the root.
  3. Use absolute values for variables when necessary.

9. Using Tables and Stat Functions on Calculators

• Steps:
  1. Use the STAT function to input data.
  2. Use diagnostic tools to identify the best fit model (linear, quadratic, exponential).
  3. Use the correct regression analysis and interpret the R-squared value.

Additional Tips

• Calculator Usage: Always keep your calculator in home screen mode for calculations.
• Multiple Choice Strategy: Use answer choices to back-calculate if necessary.
• Problem Solving: Be aware of restrictions such as domain issues with logs or division by zero.

Final Remarks

• Believe in yourself, study well, and use these strategies to succeed in your ACP exam. Good luck and see you next school year!