# Math 1314 Lab 2 Math Worksheet

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Lab 2 Math 1314 Section __________ Student Name _____________________________________________________ For each of the following problems, show all work! Simplify and clearly indicate all answers. 1. For each planet in the solar system, its year is the time it takes the planet to revolve around the 3 center star. The formula E  0.2 x 2 models the number of Earth days in a planet’s year, E, where x is the average distance of the planet from the center star, in millions of kilometers. There are approximately 88 Earth days in the year of the planet Mercury. What is the average distance of Mercury from the center star? Round to the nearest million kilometers. Clearly state your final answer in a complete sentence. 2. In psychology, it has been suggested that the number, S, of nonsense syllables that a person can repeat consecutively depends on his or her IQ score, I, according to the function S(I) = 2 I – 9. Use this relationship to estimate the IQ of a person who can repeat 10 nonsense syllables consecutively. 3. A size 36 shoe in France is size 3.5 in England. A function that converts shoe sizes 3x  94 in France to those in England is g(x)  . A size 6 shoe in the United States 4 is size 3.5 in England. A function that converts shoe sizes in England to those in the 5 United States is f(x) = x + . 2 a. Use composition of functions to find a function that converts shoe sizes in France to those in the United States. Simplify the function. b. Determine the shoe size in the United States for a size 38 shoe in France. Math 1314 Lab 2 4. For the graph g(x) below, find the indicated information. Write answers in interval notation where appropriate.                        a. Find g(5). b. State the intervals of x where the graph is increasing. c. State the intervals of x where the graph is decreasing. d. State the interval of x where the graph is constant. e. State the coordinates of the x-intercept(s). f. State the coordinates of the y-intercept. g. State the domain in interval notation. h. State the range in interval notation. i. Find any relative maxima. j. Find any relative minima. 2 Math 1314 Lab 2 5. For f(x)  3x2  5 and g(x)  7x  2 , a. Verify: g(x + 2) ≠ g(x) + g(2). b. Find (f – g)(x). c. Using the resulting function in (b), show that (f – g)(2) = f(2) – g(2). (The work should be different for each side of the equation.) f d. Is (fg)(0) =   (0)? Explain.  g e. Find f(x  h)  f(x) , h ≠ 0. h 3 Math 1314 Lab 2 4 6. Transformations: a. Write the equations of each of the following graphs. 8 8 5 7 7 4 6 6 5 5 4 4 3 3 2 2 3 2 1 -7 -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 6 7 8 9 10 -8 -7 -6 -5 -4 -3 -2 -1 -1 1 1 -1 2 3 4 5 6 7 8 9 -8 -7 -6 -5 -4 -3 -2 -1 -1 -2 -2 -2 -3 -3 -3 -4 -4 -5 -5 -6 -6 -7 -7 -8 -8 -9 -9 -4 -5 -6 1 2 3 4 5 6 7 b. The graph of a function p(x) is shown. Draw the graph of –p(x–2) + 3. 8 7 6 5 4 3 2 1 -8 -7 -6 -5 -4 -3 -2 -1 -1 1 2 3 4 5 6 7 8 9 -2 -3 -4 -5 -6 -7 -8 -9 c. Describe the transformations that have been applied to the graph of A(x) = x to obtain the graph of a(x) = 2  x . Then, sketch the graph. d. Write the equation of the function that has a graph the shape of y = 3 x , vertically shrunk by a factor of ¼ and shifted right 6 units. Then, sketch the graph. e. Write the equation of the function that has a graph the shape of y = │x│, reflected about the x-axis and shifted down 1 unit. Then, sketch the graph. f. Describe the transformations that have been applied to the graph of F(x) = x2 to obtain the graph of f(x)  (3x)2  5 . 8 9

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