Math / Algebra

QuestionHow does the graph of the transformation shown below compare to the graph of the parent function? $g(x)=-x^{4}-2$
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The parent function is $y=$ $\square$ The leading coefficient of $\square$ $\square$ $\square$ subtracting shifts the graph down 7 shifts the graph down $\square$ unit! $\square$ and (Type integers or decimals.) Help me solve this

Studdy Solution

STEP 1

What is this asking? How does flipping $x^4$ upside down and moving it down two units change its graph? Watch out! Don't mix up the negative in front of the $x^4$ and the $-2$ .
They do totally different things!

STEP 2

1. Identify the parent function.
2. Analyze the negative coefficient.
3. Analyze the vertical shift.

STEP 3

The parent function is the simplest form of the given function type.
Here, our transformed function $g(x)$ involves a variable raised to the fourth power.

STEP 4

So, the parent function is $f(x) = x^4$ .
It's like the starting point before any changes are made!

STEP 5

Now, let's look at that negative sign in front of the $x^4$ in $g(x) = -x^4 - 2$ .
This negative sign flips the graph of $x^4$ over the x-axis.

STEP 6

Imagine the parent function $x^4$ looking like a U.
The negative sign turns it upside down, like a hill or a frown!

STEP 7

Finally, we have that $-2$ hanging out at the end of $g(x) = -x^4 - 2$ .
This $-2$ causes a vertical shift.

STEP 8

Since it's $-2$ , the graph of $-x^4$ is shifted down by two units.
Every point on the flipped parabola moves down two spots!

STEP 9

The parent function is $y = x^4$ .
The leading coefficient of $-1$ flips the graph over the x-axis, and subtracting $2$ shifts the graph down $2$ units!

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Studdy Solution

STEP 1

What is this asking? How does flipping $x^4$ upside down and moving it down two units change its graph? Watch out! Don't mix up the negative in front of the $x^4$ and the $-2$ .
They do totally different things!

STEP 2

1. Identify the parent function.
2. Analyze the negative coefficient.
3. Analyze the vertical shift.

STEP 3

The parent function is the simplest form of the given function type.
Here, our transformed function $g(x)$ involves a variable raised to the fourth power.

STEP 4

So, the parent function is $f(x) = x^4$ .
It's like the starting point before any changes are made!

STEP 5

Now, let's look at that negative sign in front of the $x^4$ in $g(x) = -x^4 - 2$ .
This negative sign flips the graph of $x^4$ over the x-axis.

STEP 6

Imagine the parent function $x^4$ looking like a U.
The negative sign turns it upside down, like a hill or a frown!

STEP 7

Finally, we have that $-2$ hanging out at the end of $g(x) = -x^4 - 2$ .
This $-2$ causes a vertical shift.

STEP 8

Since it's $-2$ , the graph of $-x^4$ is shifted down by two units.
Every point on the flipped parabola moves down two spots!

STEP 9

The parent function is $y = x^4$ .
The leading coefficient of $-1$ flips the graph over the x-axis, and subtracting $2$ shifts the graph down $2$ units!

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Studdy Solution

STEP 1

What is this asking? How does flipping x4x^4x4 upside down and moving it down two units change its graph? Watch out! Don't mix up the negative in front of the x4x^4x4 and the −2-2−2.They do totally different things!

STEP 2

1. Identify the parent function.2. Analyze the negative coefficient.3. Analyze the vertical shift.

STEP 3

The **parent function** is the simplest form of the given function type.Here, our transformed function g(x)g(x)g(x) involves a variable raised to the fourth power.

STEP 4

So, the parent function is f(x)=x4f(x) = x^4f(x)=x4.It's like the starting point before any changes are made!

STEP 5

Now, let's look at that negative sign in front of the x4x^4x4 in g(x)=−x4−2g(x) = -x^4 - 2g(x)=−x4−2.This negative sign **flips** the graph of x4x^4x4 over the x-axis.

STEP 6

Imagine the parent function x4x^4x4 looking like a U.The negative sign turns it upside down, like a hill or a frown!

STEP 7

Finally, we have that −2-2−2 hanging out at the end of g(x)=−x4−2g(x) = -x^4 - 2g(x)=−x4−2.This −2-2−2 causes a **vertical shift**.

STEP 8

Since it's −2-2−2, the graph of −x4-x^4−x4 is shifted **down** by **two** units.Every point on the flipped parabola moves down two spots!

STEP 9

The parent function is y=x4y = x^4y=x4.The leading coefficient of −1-1−1 flips the graph over the x-axis, and subtracting 222 shifts the graph down 222 units!

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Studdy solves anything!

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

What is this asking? How does flipping $x^4$ upside down and moving it down two units change its graph? Watch out! Don't mix up the negative in front of the $x^4$ and the $-2$ .
They do totally different things!

1. Identify the parent function.
2. Analyze the negative coefficient.
3. Analyze the vertical shift.

The parent function is the simplest form of the given function type.
Here, our transformed function $g(x)$ involves a variable raised to the fourth power.

So, the parent function is $f(x) = x^4$ .
It's like the starting point before any changes are made!

Now, let's look at that negative sign in front of the $x^4$ in $g(x) = -x^4 - 2$ .
This negative sign flips the graph of $x^4$ over the x-axis.

Imagine the parent function $x^4$ looking like a U.
The negative sign turns it upside down, like a hill or a frown!

Finally, we have that $-2$ hanging out at the end of $g(x) = -x^4 - 2$ .
This $-2$ causes a vertical shift.

Since it's $-2$ , the graph of $-x^4$ is shifted down by two units.
Every point on the flipped parabola moves down two spots!

The parent function is $y = x^4$ .
The leading coefficient of $-1$ flips the graph over the x-axis, and subtracting $2$ shifts the graph down $2$ units!