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Exam (elaborations)

MAT 136 Exam 1 Questions and Answers
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Question Show your work and explain how you arrived at your answer. Answers with no relevant explanations do not show an understanding of the topic and may get reduced or no credit. f(g(x)) = sqrt(x^2 + 5) + 6 -Substitute g(x) into f(x) g(f(x)) = (sqrt(x) + 6)^2 + 5 -Solve for (sqrt(x) + 6)^2 ...

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  • August 9, 2024
  • 31
  • 2024/2025
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  • mat 136 exam 1 questions and answers

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12/8/2020
MAT 136 Exam 1 Questions and Answers
Question




Show your work and explain how you arrived at your answer. Answers with no relevant
explanations do not show an understanding of the topic and may get reduced or no credit.


f(g(x)) = sqrt(x^2 + 5) + 6 -Substitute g(x) into f(x)


g(f(x)) = (sqrt(x) + 6)^2 + 5 -Solve for (sqrt(x) + 6)^2


(sqrt(x) + 6)^2 = x + 12sqrt(x) +36 -Insert back to the formula


g(f(x)) = x + 12sqrt(x) +36 + 5 -Simplify
g(f(x)) = x + 12sqrt(x) +41



Keywords:

Partial Grades:


Ungraded Grade: 0/1.0 F 0%




Total grade: 1.0×1/3 + 1.0×1/3 + 0.0×1/3 = 33% + 33% + 0%
Feedback:

Let's begin by substituting g(x) into f(x).



f(g(x)) = √ (x 2 + 5 ) + 6
= √x 2 + 5 + 6
Now we can substitute f(x) into g(x).

,12/8/2020
MAT 136 Exam 1 Questions and Answers
Question




g(f(x)) = (√x + 6 )2 + 5
= x + 12√x + 36 + 5

= x + 12√x + 41




1
The graph of the function f(x) = x + 7 + 13 is a transformation of the graph of the function
1
g(x) = x by


A vertical shift
Your response Correct response
up up




units


A horizontal shift
Your response Correct response
left left

,12/8/2020
MAT 136 Exam 1 Questions and Answers
View Original Response Unfiltered Response
Q2 0/0.0 0%




Auto graded Grade: 1/1.0 A+ 100%


of
Your response Correct response
13 13

Auto graded Grade: 1/1.0 A+ 100%




Auto graded Grade: 1/1.0 A+ 100%

, 12/8/2020 Southern New Hampshire University - Gradebook

Question

of
Your response Correct response
7 7

Auto graded Grade: 1/1.0 A+ 100%


units


Show your work and explain how you arrived at your answer. Answers with no relevant
explanations do not show an understanding of the topic and may get reduced or no credit.


the vertical shift is moving the graph up and down because this transformation involves adding a positive or negative constant
to the function.


In this case, the constant is positive (13) which will move the graph up 13 units.


the horizontal is a shift that moves the graph of the function left to right.


In this case, x+7 -> x= -7. It will move 7 units to the left.

Keywords:

Partial Grades:


Ungraded Grade: 0/1.0 F 0%




Total grade: 1.0×1/5 + 1.0×1/5 + 1.0×1/5 + 1.0×1/5 + 0.0×1/5 = 20% + 20% + 20% + 20% + 0%
Feedback:
1
The graph of the function g(x) = is centered at the origin. The graph of the translated function
x
1
f(x) = x + 7 + 13 is the graph of g(x) shifted up 13 units and left 7 units. The graph of f(x) is
centered at (- 7, + 13) as x can not be equal to - 7 and y can not be equal to + 13.

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