Math / Algebra

QuestionFind $g(x)$ , where $g(x)$ is the translation 1 unit up of $f(x)=4|x+5|+8$ . Write your answer in the form $\mathrm{a}|\mathrm{x}-\mathrm{h}|+\mathrm{k}$ , where $\mathrm{a}, \mathrm{h}$ , and k are integers. $g(x)=$ Submit

Studdy Solution

STEP 1

1. We are given the function $f(x) = 4|x+5| + 8$ .
2. We need to find the function $g(x)$ which is the translation of $f(x)$ 1 unit up.
3. The answer should be in the form $a|x-h|+k$ .

STEP 2

1. Understand the effect of translating a function vertically.
2. Apply the vertical translation to $f(x)$ .
3. Express the translated function in the desired form $a|x-h|+k$ .

STEP 3

Understand that translating a function 1 unit up involves adding 1 to the entire function.

STEP 4

Apply the vertical translation to $f(x)$ :
$g(x) = f(x) + 1$
Substitute the expression for $f(x)$ :
$g(x) = 4|x+5| + 8 + 1$

STEP 5

Simplify the expression:
$g(x) = 4|x+5| + 9$

STEP 6

Express $g(x)$ in the form $a|x-h|+k$ :
Here, $a = 4$ , $h = -5$ , and $k = 9$ .
The function $g(x)$ is:
$g(x) = 4|x+5| + 9$

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QuestionFind $g(x)$ , where $g(x)$ is the translation 1 unit up of $f(x)=4|x+5|+8$ . Write your answer in the form $\mathrm{a}|\mathrm{x}-\mathrm{h}|+\mathrm{k}$ , where $\mathrm{a}, \mathrm{h}$ , and k are integers. $g(x)=$ Submit

Studdy Solution

STEP 1

1. We are given the function $f(x) = 4|x+5| + 8$ .
2. We need to find the function $g(x)$ which is the translation of $f(x)$ 1 unit up.
3. The answer should be in the form $a|x-h|+k$ .

STEP 2

1. Understand the effect of translating a function vertically.
2. Apply the vertical translation to $f(x)$ .
3. Express the translated function in the desired form $a|x-h|+k$ .

STEP 3

Understand that translating a function 1 unit up involves adding 1 to the entire function.

STEP 4

Apply the vertical translation to $f(x)$ :
$g(x) = f(x) + 1$
Substitute the expression for $f(x)$ :
$g(x) = 4|x+5| + 8 + 1$

STEP 5

Simplify the expression:
$g(x) = 4|x+5| + 9$

STEP 6

Express $g(x)$ in the form $a|x-h|+k$ :
Here, $a = 4$ , $h = -5$ , and $k = 9$ .
The function $g(x)$ is:
$g(x) = 4|x+5| + 9$

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Studdy Solution

STEP 1

1. We are given the function f(x)=4∣x+5∣+8 f(x) = 4|x+5| + 8 f(x)=4∣x+5∣+8.2. We need to find the function g(x) g(x) g(x) which is the translation of f(x) f(x) f(x) 1 unit up.3. The answer should be in the form a∣x−h∣+k a|x-h|+k a∣x−h∣+k.

STEP 2

1. Understand the effect of translating a function vertically.2. Apply the vertical translation to f(x) f(x) f(x).3. Express the translated function in the desired form a∣x−h∣+k a|x-h|+k a∣x−h∣+k.

STEP 3

Understand that translating a function 1 unit up involves adding 1 to the entire function.

STEP 4

Apply the vertical translation to f(x) f(x) f(x):g(x)=f(x)+1 g(x) = f(x) + 1 g(x)=f(x)+1Substitute the expression for f(x) f(x) f(x):g(x)=4∣x+5∣+8+1 g(x) = 4|x+5| + 8 + 1 g(x)=4∣x+5∣+8+1

STEP 5

Simplify the expression:g(x)=4∣x+5∣+9 g(x) = 4|x+5| + 9 g(x)=4∣x+5∣+9

STEP 6

Express g(x) g(x) g(x) in the form a∣x−h∣+k a|x-h|+k a∣x−h∣+k:Here, a=4 a = 4 a=4, h=−5 h = -5 h=−5, and k=9 k = 9 k=9. The function g(x) g(x) g(x) is:g(x)=4∣x+5∣+9 g(x) = 4|x+5| + 9 g(x)=4∣x+5∣+9

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1. We are given the function $f(x) = 4|x+5| + 8$ .
2. We need to find the function $g(x)$ which is the translation of $f(x)$ 1 unit up.
3. The answer should be in the form $a|x-h|+k$ .

1. Understand the effect of translating a function vertically.
2. Apply the vertical translation to $f(x)$ .
3. Express the translated function in the desired form $a|x-h|+k$ .

Apply the vertical translation to $f(x)$ :
$g(x) = f(x) + 1$
Substitute the expression for $f(x)$ :
$g(x) = 4|x+5| + 8 + 1$

Simplify the expression:
$g(x) = 4|x+5| + 9$

Express $g(x)$ in the form $a|x-h|+k$ :
Here, $a = 4$ , $h = -5$ , and $k = 9$ .
The function $g(x)$ is:
$g(x) = 4|x+5| + 9$