QuestionExplain how the function $f(x)=2|x+3|$ transforms from its parent function. (10 points)

Studdy Solution

STEP 1

Assumptions1. The given function is $f(x)=|x+3|$ . The parent function is $f(x)=|x|$
3. We are to describe the transformation of the given function from its parent function

STEP 2

The general form of a transformed absolute value function is $f(x)=a|bx+c|+d$ . Here, $a$ affects the vertical stretch or compression and reflection, $b$ affects the horizontal stretch or compression and reflection, $c$ affects the horizontal shift, and $d$ affects the vertical shift.

STEP 3

In the given function $f(x)=2|x+3|$ , we can see that $a=2$ , $b=1$ , $c=-3$ , and $d=0$ .

STEP 4

The value of $a=2$ indicates a vertical stretch by a factor of2. This means the graph of the function is stretched vertically by a factor of2 compared to the parent function.

STEP 5

The value of $b=1$ indicates no horizontal stretch or compression or reflection. This means the graph of the function remains the same horizontally as the parent function.

STEP 6

The value of $c=-3$ indicates a horizontal shift to the left by3 units. This means the graph of the function is shifted3 units to the left compared to the parent function.

STEP 7

The value of $d=0$ indicates no vertical shift. This means the graph of the function remains the same vertically as the parent function.
In conclusion, the transformation of the function $f(x)=2|x+3|$ from its parent function $f(x)=|x|$ is a vertical stretch by a factor of2 and a horizontal shift to the left by3 units.

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QuestionExplain how the function $f(x)=2|x+3|$ transforms from its parent function. (10 points)

Studdy Solution

STEP 1

Assumptions1. The given function is $f(x)=|x+3|$ . The parent function is $f(x)=|x|$
3. We are to describe the transformation of the given function from its parent function

STEP 2

The general form of a transformed absolute value function is $f(x)=a|bx+c|+d$ . Here, $a$ affects the vertical stretch or compression and reflection, $b$ affects the horizontal stretch or compression and reflection, $c$ affects the horizontal shift, and $d$ affects the vertical shift.

STEP 3

In the given function $f(x)=2|x+3|$ , we can see that $a=2$ , $b=1$ , $c=-3$ , and $d=0$ .

STEP 4

The value of $a=2$ indicates a vertical stretch by a factor of2. This means the graph of the function is stretched vertically by a factor of2 compared to the parent function.

STEP 5

The value of $b=1$ indicates no horizontal stretch or compression or reflection. This means the graph of the function remains the same horizontally as the parent function.

STEP 6

The value of $c=-3$ indicates a horizontal shift to the left by3 units. This means the graph of the function is shifted3 units to the left compared to the parent function.

STEP 7

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QuestionExplain how the function f(x)=2∣x+3∣f(x)=2|x+3|f(x)=2∣x+3∣ transforms from its parent function. (10 points)

Studdy Solution

STEP 1

Assumptions1. The given function is f(x)=∣x+3∣f(x)=|x+3|f(x)=∣x+3∣ . The parent function is f(x)=∣x∣f(x)=|x|f(x)=∣x∣3. We are to describe the transformation of the given function from its parent function

STEP 2

STEP 3

In the given function f(x)=2∣x+3∣f(x)=2|x+3|f(x)=2∣x+3∣, we can see that a=2a=2a=2, b=1b=1b=1, c=−3c=-3c=−3, and d=0d=0d=0.

STEP 4

The value of a=2a=2a=2 indicates a vertical stretch by a factor of2. This means the graph of the function is stretched vertically by a factor of2 compared to the parent function.

STEP 5

The value of b=1b=1b=1 indicates no horizontal stretch or compression or reflection. This means the graph of the function remains the same horizontally as the parent function.

STEP 6

The value of c=−3c=-3c=−3 indicates a horizontal shift to the left by3 units. This means the graph of the function is shifted3 units to the left compared to the parent function.

STEP 7

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QuestionExplain how the function $f(x)=2|x+3|$ transforms from its parent function. (10 points)

Assumptions1. The given function is $f(x)=|x+3|$ . The parent function is $f(x)=|x|$
3. We are to describe the transformation of the given function from its parent function

In the given function $f(x)=2|x+3|$ , we can see that $a=2$ , $b=1$ , $c=-3$ , and $d=0$ .

The value of $a=2$ indicates a vertical stretch by a factor of2. This means the graph of the function is stretched vertically by a factor of2 compared to the parent function.

The value of $b=1$ indicates no horizontal stretch or compression or reflection. This means the graph of the function remains the same horizontally as the parent function.

The value of $c=-3$ indicates a horizontal shift to the left by3 units. This means the graph of the function is shifted3 units to the left compared to the parent function.