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Unit 1 Study Guide Foundations for Functions NAME:____________________________________________________ DATE:________________ In this study guide, you will find a list of the topics that will be covered on the Unit 1 Test, as well as a BRIEF summary of the topic and sample test questions. This is meant to help GUIDE your STUDY for the test, not provide you with ALL of the test questions or give you answers to the test. In addition to completing this packet, you should also review your notes and graded assignments as well as re-watch the video lessons for extra help. THIS PACKET IS WORTH 100 HOMEWORK POINTS AND IS DUE ON THE DAY OF THE TEST!!! Unit 1 Topics: A) Comparing and ordering real numbers B) Evaluating expressions using substitution C) Simplifying algebraic expressions by combining like terms and using the distributive property D) Simplifying radical expressions/square roots using all operations E) Simplifying expressions using the properties of exponents F) Identifying whether a relation is a function G) Using function notation H) Performing transformations of functions Section I: Comparing Numbers, Evaluating Expressions, Simplifying Algebraic Expressions Comparing numbers: You should be able to put numbers in order from least to greatest or compare the value of two numbers, including negatives. SAMPLE PROBLEM If 2 < x < 6, which of the following has the greatest value? A) x B) x 1 C) x2 D) x 1 E) x2 Evaluating Expressions: You should be able to use substitution to evaluate an expression for a given value. SAMPLE PROBLEM What is the value of 7z2 + 4 • 3w when w= 8 and z= -3? A) 1608 B) 537 C) 412 D) 159 E) -4068 Simplifying Expressions: You should be able to simplify an algebraic expression by combining like terms. Like terms must have the SAME variable with the SAME exponent. Like terms can also be constant terms, or numbers without variables. You should also be able to use the distributive property, by multiplying the outside value to anything inside the parenthesis. Ex. 2(3x + 5) = 6x + 10 SAMPLE PROBLEM Which expression is equivalent to x 2 3 x ? A) 2( x 2 x) 3x 2 5x B) 2( x 2 x) 3x 2 5x C) 2( x 2 x) 3x 2 5x D) 2( x 2 x) 3x 2 5x Section II: Square Roots You should be able to perform all operations on square roots (addition, subtraction, multiplication and division). You should be able to simplify square roots completely and rationalize the denominator, if necessary. SAMPLE PROBLEMS Which expression is in simplest form? A) 45 3 5 B) 2 10 D) 4 30 D) 27 9 Which expression can be used to represent the area of the rectangle shown? a) 8 3 b) 2 8 c) 4 8 d) 2 12 8 24 Simplify each expression using the properties of square roots. A) 2 2 72 B) 72 4 C) 3 10 2 D) 5 125 3 Section III: Properties of Exponents You should be able to use the properties of exponents to simplify expressions. Properties of Exponents: A) When you multiply powers, add the exponents. B) When you divide powers, subtract the exponents. C) When you raise a power to a power, multiply the exponents. D) Anything to the zero power equals ONE. E) When you have a negative exponent, flip the term with the negative exponent to the opposite part of the fraction, then make the exponent positive. SAMPLE PROBLEMS Which of the following is not equivalent to a) m 2 n11 b) m 4 n12 m2n ( mn3 ) 4 ? m2n c) m 1 n11 d) (mn3 ) 4 m 2 n 1 e) m 2 (n 3 ) 4 n Which expression is equivalent to (5 x 2 y 1 z 3 ) 2 ? A) 5x 4 y2z6 B) 25 x 4 y 2 z 6 C) 25 x 4 y 2 z 6 D) 25 x 4 y2z6 What is of the volume of the cube shown? (***V= Length * Width* Height) 3d4 The table below shows the populations of select cities around the world. City Country Population Houston, TX United States 1.953 x 106 Seoul South Korea 1.023 x 107 Hong Kong China 6.843 x 106 Chicago, IL United States 2.896 x 106 Cairo Egypt 6.800 x 106 Istanbul Turkey 8.260 x 106 What statement is true about the values shown? A) The cities are arranged by least population to greatest population. B) Istanbul has the greatest population out of all of the cities shown in the table C) Chicago has a greater population than Soeul D) Hong Kong has a smaller population than Istanbul Section IV: Functions You should be able to: -Identify the domain (x-values) and range (y-values) of a function -Identify whether a relation is a function (if any of the inputs repeat with different outputs, it is NOT a function!) -Use function notation ie f(x) -Perform transformations of functions A) Translation: Slide left, right, up or down B) Reflection: Flip over a line of reflection C) Stretch: Expand the figure D) Compress: Shrink the figure SAMPLE PROBLEMS Which element is in the range of the function {(-9, -2), (2, 4), (3, -7), (8, 1), (10, 0), (5, 6)}? A) -9 B) -1 C) 2 D) 3 E) 6 Consider the function f(x) = 6x – 12. What is f(-3)? A) -216 B) -30 C) -18 D) -6 For which function does f(-8)= -6? A) f ( x) 2 x 2 6 B) f ( x) 10 x 6 C) f ( x) x 2 10 D) f ( x) 2 x 10 Refer to the table below. If the milk price is the range and the number of ounces is the domain, which statement is true for the graph of the data in the table? Package Size Number of Ounces Milk Price 1 pint 16 $0.90 1 quart 32 $1.29 1 half gallon 64 $1.95 2 quarts 64 $2.58 1 gallon 128 $3.90 A) B) C) D) The graph is a function The points form a line The graph fails the vertical line test “Milk Price” is the label for the horizontal axis For what value of x would the relation NOT be a function? x y 12 132 15 150 x 132 21 300 A) B) C) D) 15 21 132 12 A phone company charges $40 per month for the first 500 minutes plus $0.75 for each additional minute used. The expression c(m)= 40 + 0.75m can be used to find the total monthly bill. What would an input of 30 represent in this situation? A) 30 minutes have been used this month B) The monthly bill is $30 C) 530 minutes have been used this month D) The monthly bill was $530 The function c(p) = 0.99p represents the cost in dollars of p pounds of peaches. If the cost per pound increases by 10%, how will the graph of the function change? A) Translation 0.1 unit up B) Translation 0.1 unit right C) Horizontal stretch by a factor of 1.1 D) Vertical stretch by a factor of 1.1 Which transformation would change the point (5, 3) into (-5, 3)? A) Reflection across the x-axis B) Translation 5 units down C) Reflection across the y-axis D) Translation 5 units left