1010 final review.pdf - 1010 REAL Review for Final Exam Chapter 1 Function Sense 1 The notation T(c represents the amount of tuition paid depending on

1010 final review.pdf - 1010 REAL Review for Final Exam...

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1010 REAL Review for Final Exam Chapter 1: Function Sense 1) The notation T(c) represents the amount of tuition paid depending on the number of credit hours for which a student is registered. Interpret the meaning of T(12). 2) You know the point (2, 3) is on the graph of a function f. Give the coordinates of a point you know is not on the graph of the function. 3) Use what you’ve learned about solving systems of equations and solving inequalities to determine if the ordered pair (3, -5) is a solution to this system of linear inequalities ! ࠵? + 7࠵? > −1 2࠵? − 5࠵? < 4 ? Explain your answer. 4) For every function involving two variables, we designate one variable as input and the other variable as output. a) Which of these is always the dependent variable? b) On which axis (horizontal or vertical) is the dependent variable always labeled? 5) The amount of water in a leaky bucket is given by the linear function ࠵? = 126 − 4࠵? , where y is in ounces and x is in minutes. Find and interpret the slope and y-intercept of the linear equation. 6) In words, give the definition of slope and tell how slope and average rate of change are related. 7) The price of a certain commodity is a function of supply and demand. The table below shows the price of the commodity per barrel between 2005 and 2010. a) Find the average annual rate of change between 2006 and 2008. b) In terms of “average rate of change”, explain why this is or isn’t a linear function. Year Price/barrel 2005 $21 2006 $24 2007 $17 2008 $10 2009 $24 2010 $36 8) a) Graph the function f(x) = -3x + 8 as a solid line. b) Find the equation of its inverse and write it in function form. c) Graph the inverse as a dashed line on the same set of axes. d) Given that the domain and range are switched for inverse functions, how could you graph the inverse function without first finding the equation of the inverse.
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9) Solve the following system of equations. If the system is dependent or inconsistent indicate this. If not, give the solution as an ordered triplet. x + y + z = -2 x - y + 4z = -8 4x + y + z = 13 10) Solve the inequality, giving its solution set in both interval and graph forms. -4(3y + 6) < -16y + 12 Chapter 2: The Algebra of Functions/Radicals 11) Is it correct to simplify 2 3 3 2 as 6 6 ? Explain why or why not. 12) Expand (࠵? − 4) 1 . 13) Divide 3࠵? 1 − 5࠵? 3 + 10࠵? − 3 by 3࠵? + 1 14) a) Can √࠵? represent a negative real number? Why or why not? b) Can √࠵? 7 represent a negative real number? Why or why not? 15) For each of the following radicals, circle all possible reasons the given radical can’t be written as simplified radical or integer in the real number system. a) √−29 9 A) 29 isn’t divisible by 5 B) There aren’t 5 factors of the same number that multiply to get -29 C) You can’t have a negative under a radical, if so the result would be an imaginary number D) There aren’t 5 of the same factor in the prime factorization of -29 E) There isn’t a number that when raised to the 5 th power equals -29 b) √−2015 7: A) 30 isn’t a factor of -2015 B) There aren’t 30 factors of the same number that multiply to get -2015 C)
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