Extra Practice. Skills Practice. Match each situation to its ... many hours will the costs be the same? Evaluate each piecewise function for x = -2 an...
Match each situation to its corresponding graph. Sketch a possible graph of the situation if the situation does not match any of the given graphs. Graph A
Graph C
Graph B
Graph D
1. A state senator’s high approval rating is rising steadily but then drops sharply after a scandal. 2. The value of an antique chair increases steadily. 3. Sales of a valuable stock dip and then recover. 4. A scuba diver descends to 60 ft below sea level and swims around at that depth. Lesson
6-2
Compare the end behavior for each pair of functions. 5. y = – 3x2 + 10x and y = – 3(2)x
6. f (x) = e–x and g(x) = x5 + 1
7. Larry charges $40 per hour for tutoring. Tutor-Express charges as shown in the table. For how many hours will the costs be the same? Lesson
6-3
Lesson
6-4
Tutor-Express Tutoring (h)
1
2
3
4
Cost ($)
80
110
140
170
Evaluate each piecewise function for x = -2 and x = 5. ⎧ 10 8. f (x) = ⎨ 7 ⎩ 3
if x ≤ -4 if -4 < x ≤ 2 if x > 2
Graph each function. ⎧4 if x < -1 11. f (x) = ⎨ ⎩ -1 if x ≥ -1 ⎧ 2x - 2 Given f (x) = ⎨ ⎩ -3x
⎧x + 2 9. g (x) = ⎨ ⎩4 - x
if x < 0 if x ≥ 0
⎧ 2x - 4 if x ≤ 2 12. g (x) = ⎨ ⎩ -2x + 2 if x > 2
⎧ x2 - 3 10. h (x) = ⎨ ⎩x + 1
⎧2 if x < 3 13. h (x) = ⎨ 2 ⎩ x - 7 if x ≥ 3
if x < 1 , write the rule for each function. if x ≥ 1
14. g (x), a vertical stretch by a factor of 3
15. h (x), a reflection across the y-axis
Identify the x- and y-intercepts of f (x). Without graphing g (x), identify its x- and y-intercepts. 16. f (x) = -3x + 6 and g (x) = f (-2x) 17. f (x) = (x - 3) 2 and g(x) = -2f (x)
EPS12
if x ≤ 2 if x > 2
Extra Practice Chapter 6 Lesson
6-5
Skills Practice
Given f(x), graph g(x). 1 x - 4 and g (x) = f (-x) + 2 1 f (x - 1) - 4 18. f (x) = _ 19. f (x) = ⎪x + 2⎥ and g (x) = _ 2 2 2 Given f (x) = -2x + 5 and g (x) = 4x - 11, find each function. 20. (f + g)(x) 21. (f - g)(x) 22. (g - f )(x) Given f (x) = x - 3 and g (x) = x 2 + 3x - 18, find each function.
()
()
f ( ) 24. _ g x
23. (fg)(x)
g 25. _ (x) f
1 x + 5 and g(x) = -2x 2, find each value. Given f (x) = _ 2 26. f (g (2)) 27. g ( f (2))
28. g ( f (-6))
Given f(x) = √ x , g(x) = 2x + 3, and h(x) = x 2 + 20, write each composite function. State the domain of each. 29. f (g (x)) 30. g ( f (x)) 31. g (h(x)) Lesson
Use the horizontal-line test to determine whether the inverse of each relation is a function.
6-6
32.
4
33.
y
4
34.
y
4
y
2 x -4
-2
0
2
4
x -4
0
-2
2
4
x -4
-2
0
-2
-2
-2
-4
-4
-4
2
Find the inverse of each function. Determine whether the inverse is a function, and state its domain and range. 3 1x-7 35. f (x) = _ 36. g (x) = 10 - x 2 37. h (x) = _ 4+x 2 Determine by composition whether each pair of functions are inverses. 3 x 2 and g (x) = _ 4 x for x ≥ 0 38. f (x) = _ 4 3 Lesson
6-7
12x + 1 5 39. f (x) = _ and g (x) = _ 5 12x - 1
Use constant differences or ratios to determine which parent function would best model the given data set. 40. 41. 42. x
