Math 1314 Lab Module 1

Math 1314 Lab Module 1 Name _____________________ For each of the following problems, show all work! Simplify and clearly indicate all answers. 7 2D can be used to approximate the speed S, in miles per hour, of a car 2 that has left skid marks of length D, in feet. How fast would a car have been traveling if it left a skid mark that is 102.04 feet long? Round to the nearest integer. Clearly state your final answer in a complete sentence with proper grammar and correct spelling. 1. The function S(D) = 2. 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( x ) = 0.2x 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 with proper grammar and correct spelling. Math 1314 Lab Module 1 3. 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. page 2 Math 1314 4. Lab Module 1 page 3 Sketch the function that has a graph the shape of r(x) = x , reflected over the y-axis and vertically stretched by a factor of 3. Write the equation of the function. State the domain of the y transformed function in interval notation. 9 8 7 6 5 4 3 2 1 -9 -8 -7 -6 -5 -4 -3 -2 -1 5. 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 2 3 4 5 6 7 8 9 x Sketch the function that has a graph the shape of s(x) = x2, with a horizontal shrink by a factor of ⅓ and shifted up two units. Write the equation of the function. State the domain of the transformed function in interval notation. y 9 8 7 6 5 4 3 2 1 -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 -2 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 x 1 2 3 4 5 6 7 8 9 x -3 -4 -5 -6 -7 -8 -9 9 8 6. Sketch a graph of the function a(x) = ½ x + 4 . Describe the transformations to the graph of y = 7 6 5 4 3 2 1 3 3 y x. -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 -6 -7 -8 -9 9 8 y 7 6 5 4 3 2 1 7. Sketch a graph of the function c(x) = (½x)3 – 1. Describe the transformations to the graph of y = x3 -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 -6 -7 -8 -9 Math 1314 Lab Module 1 page 4 8. State the domain and range of the following function. Describe the transformations to the basic function. Then, write the equations of each of the function. 9 8 y 7 6 5 4 3 2 1 -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 1 2 3 4 5 6 7 8 9 x -2 -3 -4 -5 -6 -7 -8 -9 9. The graph of a function p(x) is shown. Draw the graph of –p(x – 1) – 3. 8 9 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 -8 -7 -6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 -6 -7 -8 -9 y 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 -6 -7 -8 -9 1 2 3 4 5 6 7 8 9 x Math 1314 10. Lab Module 1 For the function − 3 x + 5 if f(x) =   x − 1 if x 1 x 1 page 5 , 9 8 y 7 a. Evaluate f(–1) 6 5 4 b. Evaluate f(1) 3 2 1 c. Evaluate f(0) -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 1 2 3 4 5 6 7 8 9 x -2 -3 d. Evaluate f(5) -4 -5 -6 e. Graph the function. -7 -8 -9 11. Determine algebraically whether the function is even, odd or neither: g(x) = x x +3 2 ______________________ Math 1314 Lab Module 1 Name _____________________ For each of the following problems, show all work! Simplify and clearly indicate all answers. 7 2D can be used to approximate the speed S, in miles per hour, of a car 2 that has left skid marks of length D, in feet. How fast would a car have been traveling if it left a skid mark that is 102.04 feet long? Round to the nearest integer. Clearly state your final answer in a complete sentence with proper grammar and correct spelling. 1. The function S(D) = 2. 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( x ) = 0.2x 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 with proper grammar and correct spelling. Math 1314 Lab Module 1 3. 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. page 2 Math 1314 4. Lab Module 1 page 3 Sketch the function that has a graph the shape of r(x) = x , reflected over the y-axis and vertically stretched by a factor of 3. Write the equation of the function. State the domain of the y transformed function in interval notation. 9 8 7 6 5 4 3 2 1 -9 -8 -7 -6 -5 -4 -3 -2 -1 5. 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 2 3 4 5 6 7 8 9 x Sketch the function that has a graph the shape of s(x) = x2, with a horizontal shrink by a factor of ⅓ and shifted up two units. Write the equation of the function. State the domain of the transformed function in interval notation. y 9 8 7 6 5 4 3 2 1 -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 -2 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 x 1 2 3 4 5 6 7 8 9 x -3 -4 -5 -6 -7 -8 -9 9 8 6. Sketch a graph of the function a(x) = ½ x + 4 . Describe the transformations to the graph of y = 7 6 5 4 3 2 1 3 3 y x. -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 -6 -7 -8 -9 9 8 y 7 6 5 4 3 2 1 7. Sketch a graph of the function c(x) = (½x)3 – 1. Describe the transformations to the graph of y = x3 -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 -6 -7 -8 -9 Math 1314 Lab Module 1 page 4 8. State the domain and range of the following function. Describe the transformations to the basic function. Then, write the equations of each of the function. 9 8 y 7 6 5 4 3 2 1 -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 1 2 3 4 5 6 7 8 9 x -2 -3 -4 -5 -6 -7 -8 -9 9. The graph of a function p(x) is shown. Draw the graph of –p(x – 1) – 3. 8 9 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 -8 -7 -6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 -6 -7 -8 -9 y 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 -6 -7 -8 -9 1 2 3 4 5 6 7 8 9 x Math 1314 10. Lab Module 1 For the function − 3 x + 5 if f(x) =   x − 1 if x 1 x 1 page 5 , 9 8 y 7 a. Evaluate f(–1) 6 5 4 b. Evaluate f(1) 3 2 1 c. Evaluate f(0) -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 1 2 3 4 5 6 7 8 9 x -2 -3 d. Evaluate f(5) -4 -5 -6 e. Graph the function. -7 -8 -9 11. Determine algebraically whether the function is even, odd or neither: g(x) = x x +3 2 ______________________
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