a. using algebra.
b. graphing the function in the radicand and determining intervals on the x-axis for which the radicand is nonnegative.
For the following exercises, write the domain and range of each function using interval notation.
27.
Domain: ________ Range: ________
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
For the following exercises, sketch a graph of the piecewise function. Write the domain in interval notation.
38. f(x)={x+1−2x−3 if if x<−2x≥−2
39. f(x)={2x−11+x if if x<1x≥1
40. f(x)={x+1x−1 if if x<0x>0
41. f(x)={3x if if x<0x≥0
42. f(x)={x21−x if if x<0x>0
43. f(x)={x2x+2 if if x<0x≥0
44. f(x)={x+1x3ififx<1x≥1
45. f(x)={∣x∣1 if if x<2x≥2
For the following exercises, given each function f, evaluate f(−3),f(−2),f(−1), and f(0).
46. f(x)={x+1−2x−3 if if x<−2x≥−2
47. f(x)={10 if if x≤−3x>−3
48. f(x)={−2x2+35x−7 if if x≤−1x>−1
For the following exercises, given each function f, evaluate f(−1),f(0),f(2), and f(4).
49. f(x)={7x+37x+6 if if x<0x≥0
50. f(x)={x2−24+∣x−5∣ if if x<2x≥2
51. f(x)=⎩⎨⎧5x3x2ifififx<00≤x≤3x>3
For the following exercises, write the domain for the piecewise function in interval notation.
52. f(x)={x+1−2x−3 if if x<−2x≥−2
53. f(x)={x2−2−x2+2 if if x<1x>1
54. f(x)={2x−3−3x2 if if x<0x≥2
55. Graph y=x21 on the viewing window [−0.5,−0.1] and [0.1,0.5]. Determine the corresponding range for the viewing window. Show the graphs.
56. Graph y=x1 on the viewing window [−0.5,−0.1] and [0.1,0.5]. Determine the corresponding range for the viewing window. Show the graphs.
57. Suppose the range of a function f is [−5,8]. What is the range of ∣f(x)∣?
58. Create a function in which the range is all nonnegative real numbers.
59 .Create a function in which the domain is x>2.
60. The cost in dollars of making x items is given by the function C(x)=10x+500.
A. The fixed cost is determined when zero items are produced. Find the fixed cost for this item.
B. What is the cost of making 25 items?
C. Suppose the maximum cost allowed is $1500. What are the domain and range of the cost function, C(x)?
61. The height h of a projectile is a function of the time t it is in the air. The height in feet for t seconds is given by the function h(t)=−16t2+96t. What is the domain of the function? What does the domain mean in the context of the problem?
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Precalculus.Provided by: OpenStaxAuthored by: Jay Abramson, et al..Located at: https://openstax.org/books/precalculus/pages/1-introduction-to-functions.License: CC BY: Attribution. License terms: Download For Free at : http://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175..