Name: ___________________________________________ Block: ____________ Pre-Calculus Midterm Exam Review 2018 Suggested list of review concepts which is not limited to the following: Unit 1 Functions Functions and their graphs: domain and range, increasing/decreasing, positive/negative/constant, odd/even Composition of Functions Inverse functions Transformations Unit 2 Exponential and Logarithmic Functions Graphing exponential and log functions Properties of exponential and logarithmic graphs Re-writing exponential and logarithmic expressions Logarithmic Properties Solving exponential and logarithmic equations Growth and Decay/Interest/Newton’s Law of Cooling Unit 3 Rational Functions Factoring, including difference and sum of cubes Simplifying Rational Expressions Adding/Subtracting/Multiplying/Dividing Rational Expressions Solving Rational Equations Solving Rational Inequalities Graphing Rational Functions *Problem solving with Rational Functions – Average Cost, Max/Min, Area, Volume, Surface Area Unit 4 Sequences and Series Arithmetic Sequences and Series Geometric Sequences and Series Applications Review all reviews and assessments from Semester 1 as well. 1
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Pre-Calculus Final Exam Review - Ms. Miller's Math … · Web viewPre-Calculus Midterm Exam Review 2018S uggested list of review concepts which is not limited to the following: Unit
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Composition of Functions Inverse functions Transformations
Unit 2 Exponential and Logarithmic Functions Graphing exponential and log functions Properties of exponential and logarithmic graphs Re-writing exponential and logarithmic expressions Logarithmic Properties Solving exponential and logarithmic equations Growth and Decay/Interest/Newton’s Law of Cooling
Unit 3 Rational Functions Factoring, including difference and sum of cubes Simplifying Rational Expressions Adding/Subtracting/Multiplying/Dividing Rational Expressions Solving Rational Equations Solving Rational Inequalities Graphing Rational Functions *Problem solving with Rational Functions – Average Cost, Max/Min, Area, Volume, Surface
Area
Unit 4 Sequences and Series Arithmetic Sequences and Series Geometric Sequences and Series Applications
Review all reviews and assessments from Semester 1 as well.
Directions: Now, word backwards. I’ll give you the translation, you write the function.
4)
Compress the x values by dividing the x values by 2.
Horizontal shift 3 left.
Stretch the y values by factor of 5.
Reflect over the x.
Translate 6 units down. ________________________________
5) Think of f(x) as the parent function. Use the graph of f(x) to graph g(x)
a) g( x )=f ( 1
2x )+2
b) h(x) = -2f ( x + 1 )
Given the parent function and translation(s), write the function.
6)
Reflect over the y axis.
Vertical stretch by a factor of 2.3
Name: ___________________________________________ Block: ____________Translated 3 units down. _________________________________________
To find the equation of the inverse I. . .
For the inverse to be a function, the original graph must pass the ___________________.If it does not, we must restrict the domain/range.
7a) Is this function one-to-one?
b) Generate the equation of the inverse of this function, restricting the domain so that the inverse is a function. Graph the original function and its inverse, clearly labeling both.
8) Sketch the graph of the inverse of the function graphed below.
Solving Strategies Review: THE ARGUMENT CAN NEVER BE NEGATIVE!Exponential Equations - Can you create like bases and then equate exponents?Log, Log, Log. . . then condense and use the log property of equality which states:Log, log, constant. . . collect log terms. Condense. Then use the definition of a logarithm.Exponential Equations – Isolate the base. Re-write in log form and solve!Exponential Equations – take the log of both sides, then use properties to solve.Does it look like a quadratic? Factor. Solve using logs as needed.
c) A new computer that cost $1,600 has a depreciated value of $900 after 2 years. Find the value of the computer after 3 years if it depreciates exponentially.
Exponential Growth or Decay
d) Bacteria usually reproduce by a process known as binary fission. In this type of reproduction, one bacterium divides, forming two bacteria. Under ideal condition, some bacteria can reproduce every 20 minutes. Find the constant k for the growth of these types of bacteria under ideal conditions and write the growth equation.
e) Carbon 14 has a half life of 2515 years. If the amount of Carbon 14 after 1000 years is 5 grams, what was the original quantity of Carbon 14?
Newton’s Law of Cooling T is the temperature of a heated object at time t, C is the constant temperature of the surrounding medium, and k is a negative constant that is associated with the cooling object.
f) A cake removed from an oven has a temperature of 210°F. It is left to cool in a room that has a temperature of 70°F. After 30 minutes, the temperature of the cake is 140°F. Find a model for the temperature of the cake, T, after t minutes.
i. What is the temperature of the cake after 40 minutes?
ii. When will the temperature of the cake be 90°F?
14. Identify any holes, vertical asymptotes, horizontal asymptotes, and slant asymptotes of each graph. If they do not exist write none in the space provided. Accurately graph each rational function.
Name: ___________________________________________ Block: ____________APPLICATIONS OF RATIONALS
1. You have created a new type of jelly bean that you would like to market to Harry Potter World. They have requested that the packages contain 12 cubic centimeters of jelly beans, and that they be packaged in cylindrical containers. You decide to explore two situations.
A. What dimensions would minimize the amount of packaging used?
Constraint:
Function to be optimized:
Real world domain:
Work:
B. You learn that the packaging material for the base and top costs $.10 per square cm, while the cost for the lateral area is $.07 per square cm. If you want to minimize your packaging costs, What dimensions should you use for the container?