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2 years ago

Which best describes the graph of f(x) = log2(x + 3) + 2 as a transformation of the graph of g(x) = log2x?

Mathematics

2 answers:

dlinn [17]2 years ago

7 0

3 units left

2 units up

monitta2 years ago

7 0

Answer:

3 unit left and 2 unit up.

Step-by-step explanation:

Given : $f(x)= \log_2(x + 3)+2$ as a transformation of the graph of $g(x) = \log_2x$

To find : Which best describes the graph transformation?

Solution :

The parent function $g(x)=\log_2x$

with the vertex (1,0)

And the graph of $f(x)=\log_2(x + 3)+2$

with the vertex (-2.75,0)

The graph of f(x) is the translation of g(x)

Transformation to the left,

f(x)→f(x+b) , the graph of f(x) is shifted towards left by b unit.

Same as the graph g(x) is shifted towards left by 3 unit and form graph of f(x).

$f(x)= \log_2(x + 3)$

Transformation towards up,

f(x)→f(x)+a , the graph of f(x) is shifted upward by a unit.

Same as the graph g(x) is shifted upward by 2 unit and form graph of f(x).

$f(x)= \log_2(x + 3)+2$

Therefore, The description of the transformation is 3 unit left and 2 unit up.

Refer the attached graph below.

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Step-by-step explanation:

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Question:-

Reika [66]

${\huge \underline{{ \fbox \color{red}{A}}{\fbox \color{green}{n}}{\fbox \color{purple}{s}}{\fbox \color{brown}{w}}{\fbox \color{yellow}{e}}{\fbox \color{gray}{r } }}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf \red{ \dfrac{1}{2} + \dfrac{1}{4} = \dfrac{3}{4} }$

Step by step explanation :-

The only thing you have to do is add the numerator to the denominator, in this case you have to add the first ones from the front, which can be these 2+1/4, which would result in 3/4, and this is called the Commutative Property.

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It is to change different ways in order of the addends the result would be the same.

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Genrish500 [490]

We have that

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therefore

case a)
$\frac{(x+4)}{3} * \frac{x}{6}$
Is equivalent

case b)
$\frac{6}{x} * \frac{(x+4)}{3}$
Is not equivalent

case c)
$\frac{x}{6} * \frac{(x+4)}{3}$
Is equivalent

case d)
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Is not equivalent

case e)
$\frac{(2 x^{2} +4x)}{18}$
Is equivalent

Hence

the answer is

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$\frac{x}{6} * \frac{(x+4)}{3}$

$\frac{(2 x^{2} +4x)}{18}$

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