4/19/2021 Southern New Hampshire University - Gradebook
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)) = evaluate f x 2 + 9 by substituting the value of g into f
( )
f x2 + 9 = √x 2 + 9 + 8
g(f(x)) = Evaluate g (√x + 8 ) by subsitiuting in the value of f into g
g (√x + 8 ) = (√x + 8 ) 2 + 9
g (√x + 8 ) = (√x + 8 )(√x + 8 ) + 9 expand (√x + 8 )(√x + 8 ) using the FOIL method
g(√x + 8 = x + 16√x + 64 + 9
g(f(x)) = x + 16√x + 73
Ungraded Grade: 0/1.0
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 + 9 ) + 8
= √x 2 + 9 + 8
Now we can substitute f(x) into g(x).
,4/19/2021 Southern New Hampshire University - Gradebook
Question
g(f(x)) = (√x + 8 )2 + 9
= x + 16√x + 64 + 9
= x + 16√x + 73
View Original Response Unfiltered Response
Q2 0/0.0
1
The graph of the function f(x) = x-6
+ 10 is a transformation of the graph of the function
1
g(x) = by
x
A vertical shift
Your response Correct response
up up
Auto graded Grade: 1/1.0
of
Your response Correct response
10 10
Auto graded Grade: 1/1.0
units
A horizontal shift
Your response Correct response
right right
Auto graded Grade: 1/1.0
of
Your response Correct response
6 6
, 4/19/2021 Southern New Hampshire University - Gradebook
Question
Auto graded Grade: 1/1.0
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.
When you graph both functions you can see the transformation graph is shifted 10 units up on the y axis and six units to the
right on the x axis from the original
To graph y = f(x − h), shift the graph of y = f(x) right h units by adding h to the x coordinates of the points on the graph of f
To graph y = f(x) + k, shift the graph of y = f(x) up k units by adding k to the y coordinates of the points on the graph of f
Ungraded Grade: 0/1.0
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) = + 10 is the graph of g(x) shifted up 10 units and right 6 units. The graph of f(x) is
x-6
centered at (+ 6, + 10) as x can not be equal to + 6 and y can not be equal to + 10.
View Original Response Unfiltered Response
Q3 0/0.0
Analyze the graph of the function f(x) = 2|x + 5| + 8 compared to the graph of the absolute value
function g(x) = |x| .
To obtain the graph of f(x) = 2|x + 5| + 8, the graph of g(x) = |x| has been
Shifted
Your response Correct response
left left
Auto graded Grade: 1/1.0
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)) = evaluate f x 2 + 9 by substituting the value of g into f
( )
f x2 + 9 = √x 2 + 9 + 8
g(f(x)) = Evaluate g (√x + 8 ) by subsitiuting in the value of f into g
g (√x + 8 ) = (√x + 8 ) 2 + 9
g (√x + 8 ) = (√x + 8 )(√x + 8 ) + 9 expand (√x + 8 )(√x + 8 ) using the FOIL method
g(√x + 8 = x + 16√x + 64 + 9
g(f(x)) = x + 16√x + 73
Ungraded Grade: 0/1.0
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 + 9 ) + 8
= √x 2 + 9 + 8
Now we can substitute f(x) into g(x).
,4/19/2021 Southern New Hampshire University - Gradebook
Question
g(f(x)) = (√x + 8 )2 + 9
= x + 16√x + 64 + 9
= x + 16√x + 73
View Original Response Unfiltered Response
Q2 0/0.0
1
The graph of the function f(x) = x-6
+ 10 is a transformation of the graph of the function
1
g(x) = by
x
A vertical shift
Your response Correct response
up up
Auto graded Grade: 1/1.0
of
Your response Correct response
10 10
Auto graded Grade: 1/1.0
units
A horizontal shift
Your response Correct response
right right
Auto graded Grade: 1/1.0
of
Your response Correct response
6 6
, 4/19/2021 Southern New Hampshire University - Gradebook
Question
Auto graded Grade: 1/1.0
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.
When you graph both functions you can see the transformation graph is shifted 10 units up on the y axis and six units to the
right on the x axis from the original
To graph y = f(x − h), shift the graph of y = f(x) right h units by adding h to the x coordinates of the points on the graph of f
To graph y = f(x) + k, shift the graph of y = f(x) up k units by adding k to the y coordinates of the points on the graph of f
Ungraded Grade: 0/1.0
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) = + 10 is the graph of g(x) shifted up 10 units and right 6 units. The graph of f(x) is
x-6
centered at (+ 6, + 10) as x can not be equal to + 6 and y can not be equal to + 10.
View Original Response Unfiltered Response
Q3 0/0.0
Analyze the graph of the function f(x) = 2|x + 5| + 8 compared to the graph of the absolute value
function g(x) = |x| .
To obtain the graph of f(x) = 2|x + 5| + 8, the graph of g(x) = |x| has been
Shifted
Your response Correct response
left left
Auto graded Grade: 1/1.0
