Test # 1 Review. to the line x y 5. y 64x x 3. y ( x 5) 4 x 2. y x2 2 x. Á 3, 4 ˆ 2x 5y 9. x y 2 3 y x 1. Á 6,4ˆ and is perpendicular. x 9. g(t) t 10.
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1 Name: Class: Date: ID: A Test # 1 Review Short Answer 1. Find all intercepts: y 64x x 3 2. Find all intercepts: y ( x 5) 4 x 2 3. Test for symmetry with respect to each axis and to the origin. y x2 2 x 4. Find the points of intersection of the graphs of the equations: x y 2 3 y x 1 5. Find the slope of the line passing through the points 1 8, 8 ˆ Á 3 and 3 16, 1 ˆ Á Find the y-intercept of the line x 4y Find an equation of the line that passes through the point (7, 2) and has the slope m that is undefined. 8. Find an equation of the line that passes through the points (18, 7) and ( 18, 23). 9. Use the result, the line with intercepts Á a,0 ˆ and Á 0,b ˆ has the equation x a y b 1, a 0, b 0, to write an equation of the line with x-intercept: Á 8,0 ˆ and y-intercept: Á 0,7 ˆ. 10. Write an equation of the line that passes through the given point and is perpendicular to the given line. Point Line Á 1, 7 ˆ x Write an equation of the line that passes through the given point and is parallel to the given line. Point Line Á 3, 4 ˆ 2x 5y Find an equation of the line through the points of intersection of y x 2 and y 6x x Write an equation of the line that passes through the point Á 6,4ˆ and is perpendicular to the line x y Evaluate (if possible) the function f(x) x 5 at x 9. Simplify the result. 15. Let fx ( ) 14x 8. Then simplify the expression f(x) f(9). x Find the domain and range of the function g(t) t Find the domain and range of the function h(x) 11 x Determine whether y is a function of x. y 5x 2 6 1
2 Name: ID: A 19. Given f(x) cosx and g(x) x, evaluate 2 f(g(2)). 20. Determine whether the function is even, odd, or neither. 21. An open box of maximum volume is to be made from a square piece of material 22 centimeters on a side by cutting equal squares from the corners and turning up the sides (see figure). Write the volume V as a function of x, the length of the corner squares. f(x) x 2 (3 x) Complete the table and use the result to estimate the it. x 3 x 3 x 2 16x 39 x f(x) 2
3 Name: ID: A 23. Determine the following it. (Hint: Use the graph to calculate the it.) x 1 x 2 ˆ 4 Á 28. Let f(x) 3 2x 2 and g( x) x 3. Find the it. x 2 g Á f( x) ˆ 29. Find the lmit. tan x ˆ x Á Find the it. cos x x Find the it. 9x 2 36x x Find the it. x 6 x x Find the it. x 4 x 5 x Let fx ( ) 4x 2 and g( x) x 3. Find the it. x 1 g Á f( x) ˆ 31. Suppose that x c fx ( ) 11 and x c gx ( ) 3. Find the following it. x c È ÎÍ fx ( ) gx ( ) 32. Suppose that x c fx ( ) 15 and x c gx ( ) 10. Find the following it. x c È ÎÍ fx ( )gx ( ) 33. Find the it (if it exists). x 8 x 8 x Find the it (if it exists). x 5 x 4 3 x 5 3
4 Name: ID: A 35. Determine the it (if it exists). x 0 12( 1 cosx) x Determine the it (if it exists). x 0 sin 4 x x Find the it (if it exists). x x x Find the it (if it exists). x 6 x 36 x Find x 0 fx x ( ) fx ( ) x where fx ( ) 4x Use the graph as shown to determine the following its, and discuss the continuity of the function at x 3. (i) f(x) (ii) f(x) (iii) f(x) x 3 x 3 x 3 È 41. Find the it (if it exists). Note that f(x) ÎÍ x represents the greatest integer function. È 3 x x 6 ÎÍ 8 ˆ Á È 42. Find the it (if it exists). Note that f(x) ÎÍ x represents the greatest integer function. È 2x x ˆ Á ÎÍ x Find the x-values (if any) at which the function fx ( ) 13x 2 15x 15 is not continuous. Which of the discontinuities are removable? 44. Find the x-values (if any) at which fx ( ) x 3 is not continuous. x 3 4
5 Name: ID: A 45. Find the constant a such that the function fx ( ) Ï 6, x 5 Ô Ì ax b, 5 x 1 6, ÓÔ x 1 is continuous on the entire real line. 46. Find all the vertical asymptotes (if any) of the 5 graph of the function fx ( ) ( x 3) Find all the vertical asymptotes (if any) of the graph of the function f(x) x3 8 x Find the it. x 0 x 2 1 ˆ Á x 49. Use a graphing utility to graph the function fx ( ) x2 2x 4 x 3 8 it fx ( ). x 2 and determine the one-sided 5
6 Test # 1 Review Answer Section SHORT ANSWER 1. ANS: x-intercepts: (0, 0), ( 8, 0), (8, 0); y-intercept: (0, 0) PTS: 1 DIF: Easy REF: OBJ: Calculate the intercepts of an equation NOT: Section ANS: x-intercepts: ( 5, 0), ( 2, 0), (2, 0); y-intercept: (0, 10) PTS: 1 DIF: Easy REF: OBJ: Calculate the intercepts of an equation NOT: Section ANS: symmetric with respect to the origin PTS: 1 DIF: Easy REF: OBJ: Identify the type of symmetry of the graph of an equation NOT: Section ANS: Á 2, 1 ˆ, Á 1, 2 ˆ PTS: 1 DIF: Medium REF: OBJ: Calculate the points of intersection of the graphs of equations NOT: Section ANS: 42 PTS: 1 DIF: Medium REF: OBJ: Calculate the slope of a line passing through two points NOT: Section ANS: (0, 2) PTS: 1 DIF: Medium REF: OBJ: Manipulate a linear equation to determine its y-intercept NOT: Section ANS: x 7 PTS: 1 DIF: Easy REF: OBJ: Write an equation of a line given a point on the line and its slope NOT: Section 0.2 1
7 8. ANS: y 5 6 x 8 PTS: 1 DIF: Easy REF: OBJ: Write an equation of a line given two points on the line NOT: Section ANS: 7x 8y 56 0 PTS: 1 DIF: Easy REF: OBJ: Write an equation of a line given its x- and y-intercepts NOT: Section ANS: y 1 PTS: 1 DIF: Medium REF: OBJ: Write an equation of a line given a point on the line and a line to which it is parallel/perpendicular NOT: Section ANS: 2x 5y 14 PTS: 1 DIF: Medium REF: OBJ: Write an equation of a line given a point on the line and a line to which it is parallel/perpendicular NOT: Section ANS: y 3x PTS: 1 DIF: Medium REF: OBJ: Write an equation of a line through the points of intersection of quadratic equations NOT: Section ANS: x y 10 0 PTS: 1 DIF: Medium REF: b OBJ: Write an equation of a line given a point on the line and a line to which it is perpendicular NOT: Section ANS: 2 PTS: 1 DIF: Easy REF: 0.3.4a OBJ: Evaluate a function and simplify NOT: Section ANS: 14 PTS: 1 DIF: Medium REF: OBJ: Simplify a difference quotient NOT: Section 0.3 2
8 16. ANS: none of the above PTS: 1 DIF: Easy REF: OBJ: Identify the domain and range of a function NOT: Section ANS: domain: (, 6) ( 6, ) range: (, 0) (0, ) PTS: 1 DIF: Easy REF: OBJ: Identify the domain and range of a function NOT: Section ANS: yes PTS: 1 DIF: Easy REF: OBJ: Identify equations that are functions NOT: Section ANS: 1 PTS: 1 DIF: Easy REF: a OBJ: Evaluate composite functions NOT: Section ANS: neither PTS: 1 DIF: Easy REF: OBJ: Identify the type of symmetry of the graph of a function NOT: Section ANS: V x(22 2x) 2 PTS: 1 DIF: Medium REF: a OBJ: Create functions in applications MSC: Application NOT: Section ANS: PTS: 1 DIF: Medium REF: OBJ: Estimate a it from a table of values NOT: Section ANS: 5 PTS: 1 DIF: Medium REF: OBJ: Estimate the it of a function from its graph NOT: Section 1.2 3
9 24. ANS: 0 PTS: 1 DIF: Easy REF: OBJ: Evaluate a it using properties of its 25. ANS: 3 22 PTS: 1 DIF: Easy REF: OBJ: Evaluate a it using properties of its 26. ANS: 1 PTS: 1 DIF: Medium REF: OBJ: Evaluate a it using properties of its 27. ANS: 8 PTS: 1 DIF: Medium REF: c OBJ: Evaluate the it of composite functions 28. ANS: 14 PTS: 1 DIF: Medium REF: c OBJ: Evaluate the it of composite functions 29. ANS: 3 PTS: 1 DIF: Medium REF: OBJ: Evaluate the it of the function 30. ANS: 1 2 PTS: 1 DIF: Easy REF: OBJ: Evaluate a it using properties of its 31. ANS: 8 PTS: 1 DIF: Medium REF: b OBJ: Evaluate the it of a function using properties of its 32. ANS: 150 PTS: 1 DIF: Medium REF: c OBJ: Evaluate the it of a function using properties of its 4
10 33. ANS: 1 16 PTS: 1 DIF: Medium REF: OBJ: Evaluate the it of a function analytically 34. ANS: 1 6 PTS: 1 DIF: Medium REF: OBJ: Evaluate the it of a function analytically 35. ANS: 6 PTS: 1 DIF: Medium REF: OBJ: Evaluate the it of a function analytically 36. ANS: 0 PTS: 1 DIF: Medium REF: OBJ: Evaluate the it of a function analytically 37. ANS: 4 PTS: 1 DIF: Medium REF: OBJ: Evaluate the it of a difference quotient 38. ANS: 1,1,1, not continuous PTS: 1 DIF: Medium REF: 1.4.3a OBJ: Estimate a it and points of discontinuity from a graph NOT: Section ANS: 1 22 PTS: 1 DIF: Easy REF: OBJ: Evaluate one-sided its NOT: Section 1.4 5
11 40. ANS: 1 12 PTS: 1 DIF: Medium REF: OBJ: Evaluate one-sided its NOT: Section ANS: 13 PTS: 1 DIF: Medium REF: OBJ: Evaluate one-sided its NOT: Section ANS: 5 PTS: 1 DIF: Medium REF: OBJ: Evaluate one-sided its NOT: Section ANS: continuous everywhere PTS: 1 DIF: Medium REF: OBJ: Identify the removable discontinuities of a function NOT: Section ANS: fx ( ) is not continuous at x 3 and the discontinuity is nonremovable. PTS: 1 DIF: Medium REF: OBJ: Identify the removable discontinuities of a function NOT: Section ANS: a 2,b 4 PTS: 1 DIF: Medium REF: OBJ: Identify the value of a parameter to ensure a function is continuous NOT: Section ANS: x 3 PTS: 1 DIF: Easy REF: OBJ: Identify the vertical asymptotes (if any) of the graph of a function NOT: Section ANS: no vertical asymptotes PTS: 1 DIF: Medium REF: OBJ: Identify the vertical asymptotes (if any) of the graph of a function NOT: Section 1.5 6
12 48. ANS: PTS: 1 DIF: Medium REF: OBJ: Evaluate one-sided its NOT: Section ANS: PTS: 1 DIF: Medium REF: OBJ: Estimate one-sided its from a graph NOT: Section 1.5 7
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