Exponential and Logarithmic Functions Quiz

Trimester Exam Revision - Mathematics

• Lesson 6-1:

  • Identifying y-intercepts: Find the point where the function crosses the y-axis. This is done by setting x to zero.
  • Identifying asymptotes: Determine the horizontal lines a function approaches but never touches.
  • Describing transformations: Understand how functions are manipulated (shifted, stretched, or reflected).
  • Identifying domain, range, asymptotes of functions: The domain is the set of valid input values (x), and the range is the set of possible output values (y).
  • Determining if a function is growth or decay: A function is growth if its value increases over time and decay if its value decreases. Exponential functions are used to represent this.
  • Calculating future values using exponential growth/decay: Use the formula for exponential growth or decay to find the value of a quantity after a certain period.
  • Exponential growth/decay formulas: Formulas are provided to calculate exponential growth and decay.

• Lesson 6-2:

  • Finding quarterly and monthly interest rates: Formulas are provided for finding rates if interest is compounded each quarter/month.
  • Creating exponential models with two points: Formulas are supplied to derive exponential relationships given two known points.
  • Continuously compounded interest: The value of investments earning interest, compounded continuously, after a given time. Use relevant formulas.
  • Compounding Interest: Variations in how interest is added to the principal during a specified period.
  • Calculating values after a period (Compound interest): Formula is used to calculate the total amount in an account after a specific period.
  • Compounding interest calculations (annually, semi-annually, quarterly, monthly, and continuously): Understand calculation methods for different compounding frequencies.

• Lesson 6-3:

  • Converting logarithmic expressions to exponential form: Formulas given to convert logarithmic form to exponential form.
  • Evaluating logarithmic expressions: Calculations for given logarithmic expressions.
  • Solving logarithmic equations: Formulas to solve for unknown variables.
  • Solving exponential equations: Formulas to solve for unknown variables.

• Lesson 6-4:

  • Identifying asymptotes and x-intercepts of logarithmic functions: How to find horizontal lines approached but not touched by a function and the points where the function crosses the x-axis.
  • Describing transformation and asymptote of logarithmic functions: How a logarithmic function is manipulated, shifted, or reflected and the horizontal asymptotes of a log function.

• Lesson 6-5:

  • Expanding logarithmic expressions: Breaking down complex logarithmic expressions into simpler parts using the properties of logarithms.
  • Combining logarithmic expressions into a single logarithm: Combining multiple logarithmic terms into a single expression using the properties of logarithms.
  • Evaluating logarithms using the change of base formula: Determining the value of logarithms using a different base through the given formula.

• Lesson 6-6:

  • Solving exponential equations: Formulas to solve for an unknown variable in exponential equations.

• Lesson 6-7:

  • Geometric sequences: Identifying terms in geometric progression and determining related ratios.
  • Recursive definitions of geometric sequences: How to define terms in a geometric progression repeatedly.
  • Solving for terms in geometric sequences: Calculating specific terms in a sequence (geometric).
  • Identifying if a sequence is geometric: Determining if a sequence is a geometric progression.

• Series:

  • Expanding and summing series: Expand the provided series and find their sums.
  • Sigma notation: To express series in compact form using mathematical notation.

• General Remarks:

  • Exact and approximate solutions: The importance of giving both exact values (if possible) and approximation to a set level of precision.
  • Units: Be mindful of units (currency, time, etc.) when interpreting results or performing calculations.
  • Understanding Formulas: Be familiar with, and know how to use, important formulas relating to logarithmic and exponential functions.

Test your knowledge on exponential and logarithmic functions with this quiz. You'll answer questions about transformations, intercepts, and properties of logarithmic functions. Perfect for students studying calculus or advanced algebra.