James Simmons MAT-121-GS009 Assignment 6 Written Assignment 6 Answer all assigned exercises, and show all work. An asterisk indicates an exercise for which a graph pool is provided in the assignment submission link. 1. Refer to graphs A-I on page 238 of the textbook to answer the following questions. [18.75 points] a. Which one is the graph of y x ? On what interval is it increasing? G, Increases at (1,1) and (-1,1) b. Which one is the graph of y x ? What is the value of y when x = 1.5? B , y= 1.5 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? A, Increases at (1,1) decreases at (-1,-1) 2. For the following piecewise-defined function, find (a) f (3) . (See section 2.6, Example 2.) [12.5 points] a. x 2 if x 3 f ( x) 5 x if x 3 A. f(-5)=(-5)-2=10 B. f(-1)=(-1)-2=2 C. f(0)= (0)-2=0 D. f(3)=5-2=2 WA 6, p. 1 f (5) , (b) f (1) , (c) f (0) , and (d) b. 2 x if x 3 f ( x) 3 x 1 if 3 x 2 4 x if x 2 3. 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. [12.5 points] a. b. y 2 x4 3 Y=2x 4th-3 Y=2(-x)4th-3 Y=2x-3 is symmetric to X axis y x 15 Y=-x+15 -y=x+15, y=-x-15 is not symmetric 4. Graph the function.* (See section 2.7, Examples 6-8.) [12.5 points] a. y x2 3 6 4 2 4 b. y=(x+3)+2 6 3 9 6 3 5. Let and . Find each of the following. (See section 2.8, g ( x) 2 x 6 f ( x) x 2 3 Example 1.) [18.75 points] WA 6, p. 2 a. b. f(-3)+g(-5) ( f g )(5) =28+16 =44 ( fg )( 3) (( g3) 2nd+3) (-2(-3)+6) = (9+3) (6+6) =12(12)= 144 c. f (5) g Fcs= (x)2nd+3=28 - 28 G(s) = -2(3) +6=-4 6. For the following function, find (a) 28/-4= -7 f ( x h) (b) f ( x h) f ( x) , and (c) f ( x h) f ( x ) h (See section 2.8, Example 4.) [12.5 points] a. f ( x) 4 x 11 F(xth)=4(xth)+11 =4x+4g+11 F(xth)-f(x)/h= 4h+22/h b. f ( x) f(xth)-f(x)=4x+fh+11-4x+11 4h+22 1 x2 7. 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.) [12.5 points] a. f ( x) x 2 , g ( x) x 4 x 2 4 (fog)(x)=f(g(x) (gof) (x)=g(f(x) F(X to the 6th-4)+2 =2x to the 6th-8 WA 6, p. 3 . b. f ( x) x 4, g ( x) 2 x (gof)(x)=g(f(x) =g(x+2) =(x+2)4th+(x+2)2nd-4 =(x to the 4th+16+X 2nd+4-4 =x to 6th+16 WA 6, p. 4