QuestionFind the function $g$ that represents the graph of $f(x)=2x-8$ translated 5 units to the right.

Studdy Solution

STEP 1

Assumptions1. The original function is $f(x) =x -8$ . We want to translate the graph of this function5 units to the right

STEP 2

The general form for a horizontal translation of a function is $g(x) = f(x - h)$ , where $h$ is the number of units the graph is shifted to the right. If $h$ is negative, the graph is shifted to the left.

STEP 3

In this case, we want to shift the graph of the function $f(x) =2x -8$ five units to the right. So, we need to replace $x$ with $(x -5)$ in the original function. $g(x) = f(x -5)$

STEP 4

Substitute $f(x)$ with $2x -8$ in the equation.
$g(x) =2(x -) -8$

STEP 5

implify the equation by distributing the2.
$g(x) =2x -10 -8$

STEP 6

Combine like terms.
$g(x) =2x -18$ So, the function $g$ whose graph represents the translation of $f(x) =2x -8$ five units to the right is $g(x) =2x -18$ .

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QuestionFind the function $g$ that represents the graph of $f(x)=2x-8$ translated 5 units to the right.

Studdy Solution

STEP 1

Assumptions1. The original function is $f(x) =x -8$ . We want to translate the graph of this function5 units to the right

STEP 2

The general form for a horizontal translation of a function is $g(x) = f(x - h)$ , where $h$ is the number of units the graph is shifted to the right. If $h$ is negative, the graph is shifted to the left.

STEP 3

In this case, we want to shift the graph of the function $f(x) =2x -8$ five units to the right. So, we need to replace $x$ with $(x -5)$ in the original function. $g(x) = f(x -5)$

STEP 4

Substitute $f(x)$ with $2x -8$ in the equation.
$g(x) =2(x -) -8$

STEP 5

implify the equation by distributing the2.
$g(x) =2x -10 -8$

STEP 6

Combine like terms.
$g(x) =2x -18$ So, the function $g$ whose graph represents the translation of $f(x) =2x -8$ five units to the right is $g(x) =2x -18$ .

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QuestionFind the function ggg that represents the graph of f(x)=2x−8f(x)=2x-8f(x)=2x−8 translated 5 units to the right.

Studdy Solution

STEP 1

Assumptions1. The original function is f(x)=x−8f(x) =x -8f(x)=x−8 . We want to translate the graph of this function5 units to the right

STEP 2

The general form for a horizontal translation of a function is g(x)=f(x−h)g(x) = f(x - h)g(x)=f(x−h), where hhh is the number of units the graph is shifted to the right. If hhh is negative, the graph is shifted to the left.

STEP 3

In this case, we want to shift the graph of the function f(x)=2x−8f(x) =2x -8f(x)=2x−8 five units to the right. So, we need to replace xxx with (x−5)(x -5)(x−5) in the original function.g(x)=f(x−5)g(x) = f(x -5)g(x)=f(x−5)

STEP 4

Substitute f(x)f(x)f(x) with 2x−82x -82x−8 in the equation.g(x)=2(x−)−8g(x) =2(x -) -8g(x)=2(x−)−8

STEP 5

implify the equation by distributing the2.g(x)=2x−10−8g(x) =2x -10 -8g(x)=2x−10−8

STEP 6

Combine like terms.g(x)=2x−18g(x) =2x -18g(x)=2x−18So, the function ggg whose graph represents the translation of f(x)=2x−8f(x) =2x -8f(x)=2x−8 five units to the right is g(x)=2x−18g(x) =2x -18g(x)=2x−18.

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QuestionFind the function $g$ that represents the graph of $f(x)=2x-8$ translated 5 units to the right.

Assumptions1. The original function is $f(x) =x -8$ . We want to translate the graph of this function5 units to the right

The general form for a horizontal translation of a function is $g(x) = f(x - h)$ , where $h$ is the number of units the graph is shifted to the right. If $h$ is negative, the graph is shifted to the left.

In this case, we want to shift the graph of the function $f(x) =2x -8$ five units to the right. So, we need to replace $x$ with $(x -5)$ in the original function. $g(x) = f(x -5)$

Substitute $f(x)$ with $2x -8$ in the equation.
$g(x) =2(x -) -8$

implify the equation by distributing the2.
$g(x) =2x -10 -8$

Combine like terms.
$g(x) =2x -18$ So, the function $g$ whose graph represents the translation of $f(x) =2x -8$ five units to the right is $g(x) =2x -18$ .