Written Assignment 3 Answer all assigned exercises, and show all work. An asterisk indicates an exercise for which a graph pool is provided in Module Details. 1. For the points P and Q, find (a) the distance d(P,Q) and (b) the coordinates of the midpoint of the segment PQ. (See section 2.1, Examples 2 and 5(a).) [3 points] P(-4, 3), Q(2, -5) 2. Determine whether the three points are collinear. (See section 2.1, Example 4.) [3 points] (-1, 4), (-2, -1), (1, 14) 3. For the following equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation.* (See section 2.1, Examples 7 and 8.) [3 points] y x4 4. (a) Find the center-radius form of the equation of the circle, and (b) graph it.* (See section 2.2, Examples 1 and 2.) [3 points] center (-3, -2), radius 6 5. Decide whether or not the equation has a circle as its graph. If it does, give the center and the radius. If it does not, describe the graph. (See section 2.2, Examples 3-5.) [3 points] WA 3, p. 1 x 2 y 2 12 x 10 y 25 6. Decide whether the relation defines a function, and give the domain and range. (See section 2.3, Examples 1-4.) [3 points] 7. Let f ( x) 3x 4 and g ( x) x 2 4 x 1 section 2.3, Example 6.) [6 points] a. b. f (3) f (3t 2) 8. Use the graph of (d) . Find and simplify each of the following. (See f (4). WA 3, p. 2 to find each function value: (a) , (b) , (c) , and y f ( x) f (2) f (0) f (1) (See section 2.3, Example 7(d).) [3 points] 9. Determine the intervals of the domain for which the function is (a) increasing, (b) decreasing, and (c) constant. (See section 2.3, Example 9.) [3 points] 10. Graph the linear function.* Identify any constant functions. Give the domain and range. (See section 2.4, Examples 1 and 2.) [3 points] f ( x) 3 11. Find the slope of the line satisfying the given conditions. (See section 2.4, Example 5.) [3 points] through (5, 3) and (1, 7) 12. Graph the line passing through the given point and having the indicated slope.* Plot two points on the line. (See section 2.4, Example 7.) [6 points] a. through (2, 3), m b. through WA 3, p. 3 3 4 , undefined slope 9 ,2 4 13. Write an equation for the line described. Give answers in standard form. (See section 2.5, Examples 1 and 2.) [9 points] a. through (2, 4), m 1 b. through (4,3), m c. through (5,1), 3 4 undefined slope 14. Give the slope and the y-intercept of the line. (See section 2.5, Example 3.) [3 points] 2 x 3 y 16 15. Write an equation (a) in standard form and (b) in slope-intercept form for the line described. (See section 2.5, Example 6.) [6 points] a. through b. through (3, 2), (4, 4), parallel to 2x y 5 perpendicular to x4 16. Determine whether the three points are collinear by using slopes. [3 points] (0, 7), (3,5), (2, 15) 17. Refer to graphs A-I on page 238 of the textbook to answer the following questions. [9 points] a. Which one is the graph of WA 3, p. 4 y x ? On what interval is it increasing? b. Which one is the graph of y x ? What is the value of y when x = 1.5? c. Which graphs of functions decrease over part of the domain and increase over the rest of the domain? On what intervals do they increase? decrease? 18. For the following piecewise-defined function, find (a) f (3) f (5) , (b) f (1) , (c) f (0) , and (d) . (See section 2.6, Example 2.) [3 points] x 2 if x 3 f ( x) 5 x if x 3 19. Without graphing, determine whether each equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these. [6 points] a. b. y 2 x4 3 y x 15 20. Graph the function.* (See section 2.7, Examples 6-8.) [3 points] y x 3 2 21. Let and . Find each of the following. (See section 2.8, g ( x) 2 x 6 f ( x) x 2 3 Example 1.) [9 points] a. b. WA 3, p. 5 ( f g )(5) ( fg )( 3) c. f (5) g 22. For the following function, find (a) f ( x h) (b) f ( x h) f ( x) , and (c) f ( x h) f ( x ) h (See section 2.8, Example 4.) [3 points] f ( x) 4 x 11 23. Given functions f and g, find (a) and its domain, and (b) , and its ( f og )( x) ( g o f )( x) domain. (See section 2.8, Example 4.) [4 points] f ( x) x 2 WA 3, p. 6 , g ( x) x 4 x 2 4