Name: ________________________ Class: ___________________ Date: __________ Pre-AP Algebra II Review of CBA-1 (Ch. #1) Each question is equally weighted. (15 questions x 10 points each=150 Points Max) 1 Consider the graph of the function f (x) 1 . x1 Which of the following is a TRUE statement based on the graph? A) B) C) D) The domain is all real numbers: x The range is all real numbers: y The graph does not have any x- or y-intercepts. The maximum value of the function on the interval [2, 5] is 1. 2 2 Find an equation for the inverse of the function f (x) 3 3 x , and graph the inverse on the 5 2 coordinate plane. F) f G) f 1 1 (x) 5 5 x 3 2 H) f (x) 5 5 x 3 2 J) f 2 1 5 5 (x) x 2 3 1 5 5 (x) x 2 3 3 Graph the linear function f (x) 3x 3 and find the intercepts. A) C) x-intercept: (–1, 0) y-intercept: (0, – 3) x-intercept: (1, 0) y-intercept: (0, – 3) D) B) x-intercept: (–1, 0) y-intercept: (0, 3) x-intercept: (1, 0) y-intercept: (0, 3) 3 4 Graph the linear function f (x) 3x 3 and find the intercepts. F) H) x-intercept: (1, 0) y-intercept: (0, + 3) x-intercept: (–1, 0) y-intercept: (0, + 3) J) G) x-intercept: (1, 0) y-intercept: (0, –3) x-intercept: (–1, 0) y-intercept: (0, –3) 4 5 3 Consider the graph of the function f (x) x 2. Which of the following is a FALSE statement based on the graph? A) B) C) D) The domain is all real numbers: x The range is all real numbers: y The maximum value of the function on the interval [-1, 1] is -1. The graph has a y-intercepts at (0, 2). Free Response: Please show all your work. You may get a partial credit even if you cannot find the correct answer. 6 Let f(x) 6x 4 and g(x) 5x 7. Find f g and its domain and range. 7 Let f(x) 4x 5 and g( x) 7x 3. Find f g and its domain and range. 5 8 Let f(x) x 2 3 and g(x) x 2 . Find ÊÁË g û f ˆ˜¯ (2) . 3x 9 Let f(x) x 3 5 and g(x) x 3 . Find ÊÁË g û f ˆ˜¯ (2) . x 10 11 Find the inverse of the function f (x) Find the inverse of the function f (x) 2 2(x 1) 3 4 2 (x 4) 2 3 6 . 1 12 Use composition of functions to explain whether f (x ) 5(x 2) 3 x 2 and g (x ) are inverse 5 3 functions. Show your work. 13 Make a mapping diagram for the relation: {(–1, 2), (0, 1), (3, –3), (6, 3)} 14 Make a mapping diagram for the relation: {(–3, –1), (–1, –5), (0, 4), (3, –6)} 15 Let f(x) x 2 4 and g(x) x 2. Find 16 Let f(x) x 2 16 and g(x) x 4. Find 17 Find the inverse of the function f (x) 2 x 2. 3 18 Find the inverse of the function f (x) 3 x 3. 8 f and its domain and range. g f g 7 and its domain and range. 19 Let f(x) x 5 and g(x) x 2 . Find ÊÁË g û f ˆ˜¯ (1) . 20 Let f(x) x 4 and g(x) x 2 . Find ÊÁË g û f ˆ˜¯ (5) . 21 ÏÔ Ê ¸ Ô ÁÁ 1 ˆ˜˜ ÊÁÁ 1 ˆ˜˜ ÊÁÁ 3 ˆ˜˜ ÊÁÁ 2 ˆ˜˜ ÔÔ Find the domain and range of the relation: ÌÔ ÁÁ 1, ˜˜ , ÁÁ , 1 ˜˜ , ÁÁ , 0 ˜˜ , ÁÁ 2, ˜˜ ˝Ô 2 ¯ Ë 2 ¯ Ë 2 ¯ Ë 3 ¯ Ô˛ ÔÓ Ë 22 ÔÏÔ ÊÁ 1 ˆ˜ ÊÁ 1 ˆ˜ ÊÁ 2 ˆ˜ Ô¸Ô Find the domain and range of the relation: ÌÔ (1, 3), ÁÁÁ , 3 ˜˜˜ , ÁÁÁ , 0 ˜˜˜ , ÁÁÁ 2, ˜˜˜ ˝Ô ÔÓ Ë 2 ¯ Ë 2 ¯ Ë 5 ¯ Ô˛ 23 A bucket has 12 inches of water in it but there is a hole in the bottom. Use interval notation to write the domain and range of the function H (x) 12 1.5x, where x is the time the water has been leaking for (in minutes) and H (x) is the height of the water (in inches). 24 A man has to travel 20 miles. His displacement during the time is demonstrated by the function D (x) 20 5x, where x is the time (in hours) and D (x) is the distance travelled (in miles). Find the domain and range of this function 25 2 Let f (x) 4x 3 and g (x) x 2x 3. What is f g ? 26 2 Let f (x) 2x 1 and g (x) x 3x 3. What is f g ? 8