Math / Algebra

Question1. Identify the parent function. Then describe the transformations that produce the graph of $f$ . a. $f(x)=|x+9|$ b. $f(x)=5 x^{3}-8$

Studdy Solution

STEP 1

What is this asking? We need to find the simplest version of each function and then describe how to change it to get the more complicated version. Watch out! Remember the order of transformations matters!
Inside changes happen before outside changes.

STEP 2

1. Analyze Function (a)
2. Analyze Function (b)

STEP 3

Alright, let's tackle function (a): $f(x) = |x + 9|$ .
First, we identify the parent function.
It's the absolute value function, $f(x) = |x|$ !
This is our starting point.

STEP 4

Now, let's describe the transformation.
We see a $+9$ inside the absolute value.
Inside changes are horizontal shifts.
Adding $9$ shifts the graph 9 units to the left!
So, we take our parent function, slide it left $9$ units, and boom, we've got $f(x) = |x + 9|$ !

STEP 5

Now for function (b): $f(x) = 5x^3 - 8$ .
Let's identify the parent function!
This time, it's the cubic function, $f(x) = x^3$ .

STEP 6

Time to describe the transformations.
We have a $5$ multiplying the $x^3$ and a $-8$ outside.
The $5$ stretches the graph vertically by a factor of 5.
Think of it like pulling the graph upwards, making it taller and skinnier!

STEP 7

Finally, the $-8$ outside the cubic term shifts the entire graph down 8 units.
So, we stretch it vertically by a factor of $5$ and then shift it down $8$ units, and we've got our transformed function $f(x) = 5x^3 - 8$ !

STEP 8

a. Parent function: $f(x) = |x|$ .
Transformation: Horizontal shift 9 units to the left. b. Parent function: $f(x) = x^3$ .
Transformations: Vertical stretch by a factor of 5, followed by a vertical shift 8 units down.

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Question1. Identify the parent function. Then describe the transformations that produce the graph of $f$ . a. $f(x)=|x+9|$ b. $f(x)=5 x^{3}-8$

Studdy Solution

STEP 1

What is this asking? We need to find the simplest version of each function and then describe how to change it to get the more complicated version. Watch out! Remember the order of transformations matters!
Inside changes happen before outside changes.

STEP 2

1. Analyze Function (a)
2. Analyze Function (b)

STEP 3

Alright, let's tackle function (a): $f(x) = |x + 9|$ .
First, we identify the parent function.
It's the absolute value function, $f(x) = |x|$ !
This is our starting point.

STEP 4

Now, let's describe the transformation.
We see a $+9$ inside the absolute value.
Inside changes are horizontal shifts.
Adding $9$ shifts the graph 9 units to the left!
So, we take our parent function, slide it left $9$ units, and boom, we've got $f(x) = |x + 9|$ !

STEP 5

Now for function (b): $f(x) = 5x^3 - 8$ .
Let's identify the parent function!
This time, it's the cubic function, $f(x) = x^3$ .

STEP 6

Time to describe the transformations.
We have a $5$ multiplying the $x^3$ and a $-8$ outside.
The $5$ stretches the graph vertically by a factor of 5.
Think of it like pulling the graph upwards, making it taller and skinnier!

STEP 7

Finally, the $-8$ outside the cubic term shifts the entire graph down 8 units.
So, we stretch it vertically by a factor of $5$ and then shift it down $8$ units, and we've got our transformed function $f(x) = 5x^3 - 8$ !

STEP 8

a. Parent function: $f(x) = |x|$ .
Transformation: Horizontal shift 9 units to the left. b. Parent function: $f(x) = x^3$ .
Transformations: Vertical stretch by a factor of 5, followed by a vertical shift 8 units down.

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Question1. Identify the parent function. Then describe the transformations that produce the graph of fff. a. f(x)=∣x+9∣f(x)=|x+9|f(x)=∣x+9∣ b. f(x)=5x3−8f(x)=5 x^{3}-8f(x)=5x3−8

Studdy Solution

STEP 1

What is this asking? We need to find the simplest version of each function and then describe how to change it to get the more complicated version. Watch out! Remember the order of transformations matters!Inside changes happen *before* outside changes.

STEP 2

1. Analyze Function (a)2. Analyze Function (b)

STEP 3

Alright, let's tackle function (a): f(x)=∣x+9∣f(x) = |x + 9|f(x)=∣x+9∣.First, we **identify the parent function**.It's the absolute value function, f(x)=∣x∣f(x) = |x|f(x)=∣x∣!This is our starting point.

STEP 4

Now, let's **describe the transformation**.We see a +9+9+9 *inside* the absolute value.Inside changes are horizontal shifts.Adding 999 shifts the graph **9 units to the left**!So, we take our parent function, slide it left 999 units, and boom, we've got f(x)=∣x+9∣f(x) = |x + 9|f(x)=∣x+9∣!

STEP 5

Now for function (b): f(x)=5x3−8f(x) = 5x^3 - 8f(x)=5x3−8.Let's **identify the parent function**!This time, it's the cubic function, f(x)=x3f(x) = x^3f(x)=x3.

STEP 6

Time to **describe the transformations**.We have a 555 multiplying the x3x^3x3 and a −8-8−8 outside.The 555 *stretches* the graph vertically by a **factor of 5**.Think of it like pulling the graph upwards, making it taller and skinnier!

STEP 7

Finally, the −8-8−8 outside the cubic term shifts the entire graph **down 8 units**.So, we stretch it vertically by a factor of 555 and then shift it down 888 units, and we've got our transformed function f(x)=5x3−8f(x) = 5x^3 - 8f(x)=5x3−8!

STEP 8

a. Parent function: f(x)=∣x∣f(x) = |x|f(x)=∣x∣.Transformation: Horizontal shift **9 units to the left**. b. Parent function: f(x)=x3f(x) = x^3f(x)=x3.Transformations: Vertical stretch by a **factor of 5**, followed by a vertical shift **8 units down**.

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

Question1. Identify the parent function. Then describe the transformations that produce the graph of $f$ . a. $f(x)=|x+9|$ b. $f(x)=5 x^{3}-8$

What is this asking? We need to find the simplest version of each function and then describe how to change it to get the more complicated version. Watch out! Remember the order of transformations matters!
Inside changes happen before outside changes.

1. Analyze Function (a)
2. Analyze Function (b)

Alright, let's tackle function (a): $f(x) = |x + 9|$ .
First, we identify the parent function.
It's the absolute value function, $f(x) = |x|$ !
This is our starting point.

Now, let's describe the transformation.
We see a $+9$ inside the absolute value.
Inside changes are horizontal shifts.
Adding $9$ shifts the graph 9 units to the left!
So, we take our parent function, slide it left $9$ units, and boom, we've got $f(x) = |x + 9|$ !

Now for function (b): $f(x) = 5x^3 - 8$ .
Let's identify the parent function!
This time, it's the cubic function, $f(x) = x^3$ .

Time to describe the transformations.
We have a $5$ multiplying the $x^3$ and a $-8$ outside.
The $5$ stretches the graph vertically by a factor of 5.
Think of it like pulling the graph upwards, making it taller and skinnier!

Finally, the $-8$ outside the cubic term shifts the entire graph down 8 units.
So, we stretch it vertically by a factor of $5$ and then shift it down $8$ units, and we've got our transformed function $f(x) = 5x^3 - 8$ !

a. Parent function: $f(x) = |x|$ .
Transformation: Horizontal shift 9 units to the left. b. Parent function: $f(x) = x^3$ .
Transformations: Vertical stretch by a factor of 5, followed by a vertical shift 8 units down.