QuestionFind the function $g(x)$ that represents a vertical shrink of $f(x)=|x|-3$ by a factor of $\frac{1}{3}$ .

Studdy Solution

STEP 1

Assumptions1. The original function is $f(x)=|x|-3$ . The transformation is a vertical shrink by a factor of $\frac{1}{3}$

STEP 2

A vertical shrink by a factor of $\frac{1}{}$ means that each y-coordinate of the original function will be multiplied by $\frac{1}{}$ .This transformation can be represented by the function $g(x) = \frac{1}{}f(x)$ .

STEP 3

Now, we substitute $f(x)$ with $|x|-3$ in the function $g(x)$ .
$g(x) = \frac{1}{3}f(x) = \frac{1}{3}(|x|-3)$

STEP 4

Now, distribute the $\frac{1}{3}$ inside the parentheses.
$g(x) = \frac{1}{3}|x| - \frac{1}{3} \times3$

STEP 5

implify the equation.
$g(x) = \frac{1}{3}|x| -1$ So, the function $g$ whose graph represents the indicated transformation of the graph of $f$ is $g(x) = \frac{1}{3}|x| -1$ .

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QuestionFind the function $g(x)$ that represents a vertical shrink of $f(x)=|x|-3$ by a factor of $\frac{1}{3}$ .

Studdy Solution

STEP 1

Assumptions1. The original function is $f(x)=|x|-3$ . The transformation is a vertical shrink by a factor of $\frac{1}{3}$

STEP 2

A vertical shrink by a factor of $\frac{1}{}$ means that each y-coordinate of the original function will be multiplied by $\frac{1}{}$ .This transformation can be represented by the function $g(x) = \frac{1}{}f(x)$ .

STEP 3

Now, we substitute $f(x)$ with $|x|-3$ in the function $g(x)$ .
$g(x) = \frac{1}{3}f(x) = \frac{1}{3}(|x|-3)$

STEP 4

Now, distribute the $\frac{1}{3}$ inside the parentheses.
$g(x) = \frac{1}{3}|x| - \frac{1}{3} \times3$

STEP 5

implify the equation.
$g(x) = \frac{1}{3}|x| -1$ So, the function $g$ whose graph represents the indicated transformation of the graph of $f$ is $g(x) = \frac{1}{3}|x| -1$ .

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QuestionFind the function g(x)g(x)g(x) that represents a vertical shrink of f(x)=∣x∣−3f(x)=|x|-3f(x)=∣x∣−3 by a factor of 13\frac{1}{3}31​.

Studdy Solution

STEP 1

Assumptions1. The original function is f(x)=∣x∣−3f(x)=|x|-3f(x)=∣x∣−3 . The transformation is a vertical shrink by a factor of 13\frac{1}{3}31​

STEP 2

A vertical shrink by a factor of 1\frac{1}{}1​ means that each y-coordinate of the original function will be multiplied by 1\frac{1}{}1​.This transformation can be represented by the function g(x)=1f(x)g(x) = \frac{1}{}f(x)g(x)=1​f(x).

STEP 3

Now, we substitute f(x)f(x)f(x) with ∣x∣−3|x|-3∣x∣−3 in the function g(x)g(x)g(x).g(x)=13f(x)=13(∣x∣−3)g(x) = \frac{1}{3}f(x) = \frac{1}{3}(|x|-3)g(x)=31​f(x)=31​(∣x∣−3)

STEP 4

Now, distribute the 13\frac{1}{3}31​ inside the parentheses.g(x)=13∣x∣−13×3g(x) = \frac{1}{3}|x| - \frac{1}{3} \times3g(x)=31​∣x∣−31​×3

STEP 5

implify the equation.g(x)=13∣x∣−1g(x) = \frac{1}{3}|x| -1g(x)=31​∣x∣−1So, the function ggg whose graph represents the indicated transformation of the graph of fff is g(x)=13∣x∣−1g(x) = \frac{1}{3}|x| -1g(x)=31​∣x∣−1.

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QuestionFind the function $g(x)$ that represents a vertical shrink of $f(x)=|x|-3$ by a factor of $\frac{1}{3}$ .

Assumptions1. The original function is $f(x)=|x|-3$ . The transformation is a vertical shrink by a factor of $\frac{1}{3}$

A vertical shrink by a factor of $\frac{1}{}$ means that each y-coordinate of the original function will be multiplied by $\frac{1}{}$ .This transformation can be represented by the function $g(x) = \frac{1}{}f(x)$ .

Now, we substitute $f(x)$ with $|x|-3$ in the function $g(x)$ .
$g(x) = \frac{1}{3}f(x) = \frac{1}{3}(|x|-3)$

Now, distribute the $\frac{1}{3}$ inside the parentheses.
$g(x) = \frac{1}{3}|x| - \frac{1}{3} \times3$

implify the equation.
$g(x) = \frac{1}{3}|x| -1$ So, the function $g$ whose graph represents the indicated transformation of the graph of $f$ is $g(x) = \frac{1}{3}|x| -1$ .