QuestionFind the function $g(x)$ that results from a vertical shrink of $f(x)=2x+6$ by a factor of $\frac{1}{2}$ .

Studdy Solution

STEP 1

Assumptions1. The original function is $f(x) =x +6$ . The transformation is a vertical shrink by a factor of $\frac{1}{}$

STEP 2

A vertical shrink by a factor of $\frac{1}{2}$ means that the y-values of the original function are halved. This can be achieved by multiplying the original function by the factor $\frac{1}{2}$ .
$g(x) = \frac{1}{2} \cdot f(x)$

STEP 3

Now, substitute the original function $f(x) =2x +6$ into the transformation equation.
$g(x) = \frac{1}{2} \cdot (2x +6)$

STEP 4

implify the equation by distributing the $\frac{1}{2}$ to both terms inside the parentheses.
$g(x) = \frac{1}{2} \cdot2x + \frac{1}{2} \cdot6$

STEP 5

implify further by performing the multiplication.
$g(x) = x +3$ The transformed function is $g(x) = x +3$ .

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QuestionFind the function $g(x)$ that results from a vertical shrink of $f(x)=2x+6$ by a factor of $\frac{1}{2}$ .

Studdy Solution

STEP 1

Assumptions1. The original function is $f(x) =x +6$ . The transformation is a vertical shrink by a factor of $\frac{1}{}$

STEP 2

A vertical shrink by a factor of $\frac{1}{2}$ means that the y-values of the original function are halved. This can be achieved by multiplying the original function by the factor $\frac{1}{2}$ .
$g(x) = \frac{1}{2} \cdot f(x)$

STEP 3

Now, substitute the original function $f(x) =2x +6$ into the transformation equation.
$g(x) = \frac{1}{2} \cdot (2x +6)$

STEP 4

implify the equation by distributing the $\frac{1}{2}$ to both terms inside the parentheses.
$g(x) = \frac{1}{2} \cdot2x + \frac{1}{2} \cdot6$

STEP 5

implify further by performing the multiplication.
$g(x) = x +3$ The transformed function is $g(x) = x +3$ .

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QuestionFind the function g(x)g(x)g(x) that results from a vertical shrink of f(x)=2x+6f(x)=2x+6f(x)=2x+6 by a factor of 12\frac{1}{2}21​.

Studdy Solution

STEP 1

Assumptions1. The original function is f(x)=x+6f(x) =x +6f(x)=x+6 . The transformation is a vertical shrink by a factor of 1\frac{1}{}1​

STEP 2

A vertical shrink by a factor of 12\frac{1}{2}21​ means that the y-values of the original function are halved. This can be achieved by multiplying the original function by the factor 12\frac{1}{2}21​.g(x)=12⋅f(x)g(x) = \frac{1}{2} \cdot f(x)g(x)=21​⋅f(x)

STEP 3

Now, substitute the original function f(x)=2x+6f(x) =2x +6f(x)=2x+6 into the transformation equation.g(x)=12⋅(2x+6)g(x) = \frac{1}{2} \cdot (2x +6)g(x)=21​⋅(2x+6)

STEP 4

implify the equation by distributing the 12\frac{1}{2}21​ to both terms inside the parentheses.g(x)=12⋅2x+12⋅6g(x) = \frac{1}{2} \cdot2x + \frac{1}{2} \cdot6g(x)=21​⋅2x+21​⋅6

STEP 5

implify further by performing the multiplication.g(x)=x+3g(x) = x +3g(x)=x+3The transformed function is g(x)=x+3g(x) = x +3g(x)=x+3.

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QuestionFind the function $g(x)$ that results from a vertical shrink of $f(x)=2x+6$ by a factor of $\frac{1}{2}$ .

Assumptions1. The original function is $f(x) =x +6$ . The transformation is a vertical shrink by a factor of $\frac{1}{}$

A vertical shrink by a factor of $\frac{1}{2}$ means that the y-values of the original function are halved. This can be achieved by multiplying the original function by the factor $\frac{1}{2}$ .
$g(x) = \frac{1}{2} \cdot f(x)$

Now, substitute the original function $f(x) =2x +6$ into the transformation equation.
$g(x) = \frac{1}{2} \cdot (2x +6)$

implify the equation by distributing the $\frac{1}{2}$ to both terms inside the parentheses.
$g(x) = \frac{1}{2} \cdot2x + \frac{1}{2} \cdot6$

implify further by performing the multiplication.
$g(x) = x +3$ The transformed function is $g(x) = x +3$ .