AnswersPBCSD_Grade_Forgiveness_1200710_Mathematics_for_College_Algebra_S1_2023Combinations and Separations of Functions

Combinations and Separations of Functions Answers

3 verified answers
1
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If the functions are combined using addition, which statements describe the resulting graph h(x)? Check two options.

A
domain: x ≥ –2
B
domain: x ≥ 2
C
The point (2, 2) is on h(x).
D
The point (–2, 0) is on h(x).
E
The point (0, –3) is on h(x).
2
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The table shows three functions and their output values for different values of x.

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Option A
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Option B
C
h(x) = f(x) – g(x)
D
h(x) = g(x) – f(x)
3

The graph shows two functions, f(x) and g(x).If the functions are combined so that h(x) = f(x) – g(x), then the domain of the function h(x) is x ≥ .

Answer not available
4

An isosceles right triangle has a hypotenuse length that can be modeled with the function . The combined length of the legs can be modeled with the function L(x) = 2x.Which function, p(x), can be used to find the perimeter of the triangle?

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Option D
5

Consider the following functions.f(x) = x2 – 4 g(x) = x – 2What is (f(x))(g(x))?

A
(f(x))(g(x)) = x + 2; x ≠ 2
B
(f(x))(g(x)) = x + 2; all real numbers
Option B
C
(f(x))(g(x)) = x3 – 2x2 – 4x + 8; x ≠ 2
D
(f(x))(g(x)) = x3 – 2x2 – 4x + 8; all real numbers
Option D
6

Which graph shows ?

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Option A
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Option D
7

The table gives the volume of cylinders where the height is a function of the radius of the base. Given radius, r, the height can be modeled with the function h(r), the base area of the of the cylinder with the function B(r), and the volume of the cylinder with the function V(r).

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8

On a given day, the temperature in a pool increases with both the work of a heater modeled by the function h(t) and the Sun s(t), depending on the amount of time that passes, t, in minutes.Which graph best shows the combination of both functions, c(t)?

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Option D
9

An airplane company is determining the difference in selling price if rows of first-class seats are added to a new design. Using the average selling price of $1,000 per first-class seat, the total selling price for one new row is f(r) = 4,000r. Each row in first class eliminates two rows of economy seats. Using the average selling price of $150 per economy seat, the total price for each pair of removed rows is e(r) = 1,800r.

A
d(r) = 2,200r
B
d(r) = 5,800r
C
d(r) = –2,200r
D
d(r) = –5,800r
10

The function f(t) = –16t2 + 250 represents the distance of a dropped object from the ground at any time, t. The equation g(t) = 15t represents the height of the object if it is tossed upward at a rate of 15 feet per second. The sum of the functions can be used to model the distance the dropped object is from the ground if it is tossed upward at a rate of 15 feet per second before it begins its descent.

A
h(t) = –16t2 + 265t
B
h(t) = –16t2 + 235t
C
h(t) = –16t2 – 15t + 250
D
h(t) = –16t2 + 15t + 250

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