Test Name: Chapter 4 Test Prep

Transcription

1 Test Name: Chapter 4 Test Prep 1. Given the following function: g ( x ) = -x + 2 Determine the implied domain of the given function. Express your answer in interval notation. 2. Given the following relation: Step 1. Describe the domain and range for the relation. R = { (-4-1) (-3-4) (-4 1 ) (-5-3) } Step 2. Determine if the given relation is a function. If it is not, identify two ordered pairs as proof. 3. Given the following function: f ( x ) = x Determine the implied domain of the given function. Express your answer in interval notation. 4. Given the following relation: Step 1. Describe the domain and range for the relation. x = -5 Step 2. Determine if the given relation is a function. If it is not, identify two ordered pairs as proof. Answer: Function: A) yes B) no 1

2 11. Consider the following quadratic function. Reduce all fractions to the lowest terms. Step 1. Find the vertex of this function. r ( x ) = x 2 + 7x + 10 Step 2. Determine the number of x-intercept(s), then write the x-intercept(s), if any, of this function as ordered pair(s) below. Step 3. Graph this quadratic function by identifying two points on the parabola other than the vertex and the x-intercepts. Also, write the two points as ordered pairs in the spaces provided. B: (, ) 12. Consider the following linear function. Reduce all fractions to lowest terms. h ( x ) = x Step 1. Find the slope and the y-intercept (written as an ordered pair) of the line, which is represented by this function. Step 2. Graph this linear function by plotting two points on the line. Also, write the two points as ordered pairs in the spaces provided. B: (, ) 2

3 13. Find the linear function with the following properties. f( -7) = 7 and the slope of f equals Consider the following quadratic function. Step 1. Find the vertex of this function. r ( x ) = ( x - 2 ) 2 Step 2. Determine the number of x-intercept(s), then write the x-intercept(s), if any, of this function as ordered pair(s) below. Step 3. Graph this quadratic function by identifying two points on the parabola other than the vertex and the x-intercepts. Also, write the two points as ordered pairs in the spaces provided. B: (, ) 20. Consider the following quadratic function. Step 1. Find the vertex of this function. q ( x ) = ( x - 4 ) Step 2. Determine the number of x-intercept(s), then write the x-intercept(s), if any, of this function as ordered pair(s) below. Step 3. Graph this quadratic function by identifying two points on the parabola other than the vertex and the x-intercepts. 3

4 21. The total revenue for Jane's Vacation Rentals is given as the function R( x ) = 300x - 0.2x 2, where x is the number of apartments filled. What number of apartments filled produces the maximum revenue? 22. An arrow is launched upward with a velocity of 64 feet per second from the top of a 55-foot stage. What is the maximum height attained by the arrow? 24. The revenue function for a bicycle shop is given by R( x ) = x p( x ) dollars where x is the number of units sold and p( x ) = x is the unit price. Find the maximum revenue. 25. Consider the following function. s( x ) = 5 2x Step 1. Indicate the general shape of the graph of the given function. Select the appropriate graph below. Step 2. Find two points on the graph of this function, other than the origin (0, 0), and use these points to plot the graph of the function. B: (, ) 4

5 27. Consider the following function. t( x ) = - 2 x 3 Step 1. Indicate the general shape of the graph of the given function. Select the appropriate graph below. Step 2. Find two points on the graph of this function, other than the origin (0, 0), and use these points to plot the graph of the function. (Round off to two decimal places.) B: (, ) 30. Consider the following function. f( x ) = - 3 4x 6 Indicate the general shape of the graph of the given function. Select the appropriate graph below. 5

6 35. Consider the following function. p ( x ) = 2 x Step 1. Identify the more basic function that has been shifted, reflected, stretched, or compressed. Step 2. Indicate the shape of the function that was found in step 1. Step 3. Graph this function by indicating how the basic function found in step 1 has been shifted, reflected, stretched, or compressed. When necessary, indicate the units shifted and/or the factor for streching or compressing. Horizontal Shift A) Left B) Right C) None Stretch/Compress x-axis Reflection y-axis Reflection Vertical Shift A) Stretch B) Compress C) None A) Up B) Down C) None Step 4. Determine the domain and range of this function. Write your answer in interval notation or symbol notation. 40. Consider the following function. q ( x ) = ( x - 6) 3 Step 1. Identify the more basic function that has been shifted, reflected, stretched, or compressed. Step 2. Indicate the shape of the function that was found in step 1. 6

7 Step 3. Graph this function by indicating how the basic function found in step 1 has been shifted, reflected, stretched, or compressed. When necessary, indicate the units shifted and/or the factor for streching or compressing. Horizontal Shift A) Left B) Right C) None Stretch/Compress x-axis Reflection y-axis Reflection Vertical Shift A) Stretch B) Compress C) None A) Up B) Down C) None Step 4. Determine the domain and range of this function. Write your answer in interval notation or symbol notation. 42. Find a formula for the inverse of the given function. q ( x ) = 5 2x Find a formula for the inverse of the given function. G ( x ) = -3x Given the following relation: S = { ( ) ( 10-6 ) ( -2 7 ) ( -5 5 ) } Step 1. Enter the inverse of the above relation. Step 2. Enter the domain and range of the inverse. 46. Find a formula for the inverse of the given function. 1 s ( x ) = x Given 2 f ( x) 3x x and ( ) 4 g x x evaluate each of the following: a) f ( 7) b) ( f g )(3) c) ( f g )( 4) d) ( f f)(4) e) gg ( ( 1)) f. g 1 ( g ( 1)) 7