SECTION 2.2 The Graph of a Function 77 Explaining Concepts 124. Are the functions ( ) = − f x x 1 and ( ) = − + g x x x 1 1 2 the same? Explain. 125. Find a function H that multiplies a number x by 3 and then subtracts the cube of x and divides the result by your age. 126. Investigate when, historically, the use of the function notation ( ) = y f x first appeared. Retain Your Knowledge Problems 127–135 are based on previously learned material. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for subsequent sections, a final exam, or later courses such as calculus. 127. List the intercepts and test for symmetry the graph of ( ) + + = x y 12 16 2 2 128. Determine which of the given points are on the graph of the equation = − y x x 3 8 . 2 Points: ( ) ( ) ( ) − − 1, 5 , 4,32 , 9,171 129. How many pounds of lean hamburger that is 7% fat must be mixed with 12 pounds of ground chuck that is 20% fat to have a hamburger mixture that is 15% fat? 130. Solve − = − x x x 9 2 18. 3 2 131. Given + = + a bx ac d, solve for a. 132. Rotational Inertia The rotational inertia of an object varies directly with the square of the perpendicular distance from the object to the axis of rotation. If the rotational inertia is ⋅ 0.4 kg m2 when the perpendicular distance is 0.6 m, what is the rotational inertia of the object if the perpendicular distance is 1.5 m? 133. Find the slope of a line perpendicular to the line − = x y 3 10 12 134. Simplify ( ) ( ) ( ) − ⋅ − + ⋅ − x x x x 4 7 3 3 5 8 4 7 . 2 2 2 135. Determine the degree of the polynomial ( )( ) − + x x x 9 3 5 5 1 2 4 ‘Are You Prepared?’ Answers 1. ( ) −1, 3 2. 21.5 3. { } ≠ − x x 4 4. { } <− x x 1 1 1 0 5. + 5 2 6. radicals 2.2 The Graph of a Function Now Work the ‘Are You Prepared?’ problems on page 81. • Graphs of Equations (Section 1.1, pp. 4–8) • Intercepts (Section 1.3, pp. 20–21) PREPARING FOR THIS SECTION Before getting started, review the following: Year Price Year Price Year Price 1998 1.55 2007 3.31 2016 2.19 1999 1.67 2008 3.70 2017 2.38 2000 2.11 2009 2.68 2018 2.25 2001 1.97 2010 3.12 2019 2.26 2002 1.83 2011 3.84 2020 2.24 2003 2.07 2012 3.87 2021 3.13 2004 2.40 2013 3.68 2022 3.51 2005 2.85 2014 3.48 2023 3.11 2006 3.13 2015 2.51 2024 3.34 Source: U.S. Bureau of Labor Statistics. Table 2 Average Price of Gasoline Figure 17 Average retail price of gasoline (2024 dollars) 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 2022 2024 3.50 4.00 4.50 3.00 2.50 2.00 Price (dollars per gallon) 1.50 0.50 0.00 1.00 OBJECTIVES 1 Identify the Graph of a Function (p. 78) 2 Obtain Information from or about the Graph of a Function (p. 78) In Section 1.3 we saw how a graph can more clearly demonstrate the relationship between two variables. Consider the average gasoline price data and corresponding graph provided again for convenience in Table 2 and Figure 17.
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