QuestionIdentify the parent function and transformations for $g(x)=|x+3|+6$ . Options for parent function: $y=x^{2}$ , $y=x^{3}$ , $y=|x|$ , $y=\sqrt{x}$ , $y=\sqrt[3]{x}$ .

Studdy Solution

STEP 1

Assumptions1. The function is $g(x)=|x+3|+6$ . We need to identify the parent function and the transformations applied to it.

STEP 2

The parent function is the simplest form of the given function. Looking at the function $g(x)=|x+|+6$ , we can see that the parent function is $y=|x|$ . This is because the absolute value function is the simplest form of the given function.
So, the correct parent function is $y=|x|$ .

STEP 3

Next, we need to identify the transformations applied to the parent function. The general form of the absolute value function with transformations is $y=a|bx-h|+k$ , where- $a$ determines vertical stretches or compressions and reflections over the x-axis. - $b$ determines horizontal stretches or compressions and reflections over the y-axis. - $h$ determines horizontal shifts. - $k$ determines vertical shifts.

STEP 4

Looking at the function $g(x)=|x+3|+6$ , we can see that $a=1$ , $b=1$ , $h=-3$ , and $k=6$ .

STEP 5

Since $a=1$ , there is no vertical stretch or compression, and there is no reflection over the x-axis. So, there is no transformation for part (b) and part (c).

STEP 6

Since $h=-3$ , there is a horizontal shift of3 units to the left. So, the correct transformation for part (e) is a horizontal shift of3 units to the left.

STEP 7

Since $k=6$ , there is a vertical shift of6 units upwards. So, the correct transformation for part (d) is a vertical shift of6 units upwards.
To summarizea) The correct parent function is $y=|x|$ . b) There is no reflection. c) There is no stretch or compression. d) The correct vertical shift is6 units upwards. e) The correct horizontal shift is3 units to the left.

Was this helpful?

QuestionIdentify the parent function and transformations for $g(x)=|x+3|+6$ . Options for parent function: $y=x^{2}$ , $y=x^{3}$ , $y=|x|$ , $y=\sqrt{x}$ , $y=\sqrt[3]{x}$ .

Studdy Solution

STEP 1

Assumptions1. The function is $g(x)=|x+3|+6$ . We need to identify the parent function and the transformations applied to it.

STEP 2

The parent function is the simplest form of the given function. Looking at the function $g(x)=|x+|+6$ , we can see that the parent function is $y=|x|$ . This is because the absolute value function is the simplest form of the given function.
So, the correct parent function is $y=|x|$ .

STEP 3

STEP 4

Looking at the function $g(x)=|x+3|+6$ , we can see that $a=1$ , $b=1$ , $h=-3$ , and $k=6$ .

STEP 5

Since $a=1$ , there is no vertical stretch or compression, and there is no reflection over the x-axis. So, there is no transformation for part (b) and part (c).

STEP 6

Since $h=-3$ , there is a horizontal shift of3 units to the left. So, the correct transformation for part (e) is a horizontal shift of3 units to the left.

STEP 7

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionIdentify the parent function and transformations for g(x)=∣x+3∣+6g(x)=|x+3|+6g(x)=∣x+3∣+6. Options for parent function: y=x2y=x^{2}y=x2, y=x3y=x^{3}y=x3, y=∣x∣y=|x|y=∣x∣, y=xy=\sqrt{x}y=x​, y=x3y=\sqrt[3]{x}y=3x​.

Studdy Solution

STEP 1

Assumptions1. The function is g(x)=∣x+3∣+6g(x)=|x+3|+6g(x)=∣x+3∣+6 . We need to identify the parent function and the transformations applied to it.

STEP 2

STEP 3

STEP 4

Looking at the function g(x)=∣x+3∣+6g(x)=|x+3|+6g(x)=∣x+3∣+6, we can see that a=1a=1a=1, b=1b=1b=1, h=−3h=-3h=−3, and k=6k=6k=6.

STEP 5

Since a=1a=1a=1, there is no vertical stretch or compression, and there is no reflection over the x-axis. So, there is no transformation for part (b) and part (c).

STEP 6

Since h=−3h=-3h=−3, there is a horizontal shift of3 units to the left. So, the correct transformation for part (e) is a horizontal shift of3 units to the left.

STEP 7

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionIdentify the parent function and transformations for $g(x)=|x+3|+6$ . Options for parent function: $y=x^{2}$ , $y=x^{3}$ , $y=|x|$ , $y=\sqrt{x}$ , $y=\sqrt[3]{x}$ .

Assumptions1. The function is $g(x)=|x+3|+6$ . We need to identify the parent function and the transformations applied to it.

Looking at the function $g(x)=|x+3|+6$ , we can see that $a=1$ , $b=1$ , $h=-3$ , and $k=6$ .

Since $a=1$ , there is no vertical stretch or compression, and there is no reflection over the x-axis. So, there is no transformation for part (b) and part (c).

Since $h=-3$ , there is a horizontal shift of3 units to the left. So, the correct transformation for part (e) is a horizontal shift of3 units to the left.