Mathematics, 01.10.2019 17:20 spalmer7

Which is one of the transformations applied to the graph of f(x)=x2 to change it into the graph of g(x) = –x2 + 16x – 44?

the graph of f(x) = x2 is widened.
the graph of f(x) = x2 is shifted left 8 units.
the graph of f(x) = x2 is shifted down 44 units.
the graph of f(x) = x2 is reflected over the x-axis.

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Answer from: Melleeroo

D.The graph of f(x)=x^2 is reflected over the x- axis.

Step-by-step explanation:

We are given that a graph

f(x)=x^2

Change into graph of

g(x)=-x^2+16x-44

The g(x) can be written as

g(x)=-(x^2-16x+44)=-(x^2-16x+64-64+44)

g(x)=-((x-8)^2-20)

Now, the function is translated 8 units towards right by the rule of transformation is given by

$f(x)\rightarrow f(x-8)$

By using this rule

f'(x)=(x-8)^2

Now, translated the graph 20 units down by the rule of transformation is given by

$f(x)\rightarrow f(x)-20$

By using this rule

f''(x)=(x-8)^2-20

When f(x) is reflected over the x- axis then the rule of transformation is given by

$f(x)\rightarrow -f(x)$

Apply this rule then we get

g(x)=-((x-8)^2-20)=-(x-8)^2+20

Hence, the graph of f(x)=x^2 is reflected over the x- axis.

Option D is true.

Which is one of the transformations applied to the graph of f(x)=x2 to change it into the graph of g

Answer from: Quest

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2:

(2 x^3 + 7 x^2 + (x + 4 x) + 2)/(x (x + 2))

x + 4 x = 5 x:

answer: (2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

Answer from: Quest

i'm sure goog can you get that answer

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