Describe the transformation of each function compared to its parent function. I need help please!

Transformation involves changing the position and/or size of a function.

The transformations are:

The above function is a square function, and the parent function is:

First, the function is translated right by 4 units (this is represented by subtracting 4 from x.

i.e.

Next, the function is translated up by 9 units (this is represented by adding 9 to the value of y.

i.e.

So, the transformation from the parent function is: Translate f(x), 4 units right, and 9 units up.

The above function is a square function, and the parent function is:

First, the function is translated left by 4 units (this is represented by adding 4 from x.

i.e.

Next, the function is vertically compressed a factor of 1/4 (this is represented by multiplying the function by 1/4

i.e.

So, the transformation from the parent function is: Translate f(x), 4 units left, then compress f(x) vertically by 1/4

The above function is a square function, and the parent function is:

The function is vertically stretched a factor of 3/2 (this is represented by multiplying the function by 3/2

i.e.

So, the transformation from the parent function is: Vertically stretch f(x) by 3/2

Read more about transformations at:

link

Step-by-step explanation:

In general, for all problems like this, remember the acronym VOHI:

vertical outside, horizontal inside.

1. The parent function here would be . 4 has been subtracted from the inside, so it is a horizontal change. You might think that it is moving left 4, but it's actually moving right 4. There is a reason for this, but it's not necessary for you to know right now. All you need to remember is that when inside the parentheses, minus means moving right, and plus means moving left. You also have a 9 added to the outside. Vertical outside. This is a vertical change, meaning up and down. This function has been moved right 4 and up 9.

2. First, the parent function is again . This time, we have on the outside of our function. This means it is a vertical transformation. When the value on the outside is > 1, it is a vertical stretch. When the value is between 0 and 1 (0<a<1), it is a vertical shrink. is between 0 and 1. So, this is a vertical shrink by a factor of . Next, there is a 6 on the inside of the parentheses, meaning a horizontal translation. Remember from problem 1, though, minus=right and plus=left. So, this function has been vertically shrunk by and moved left 6.

3. Again, parent function: . This one just has on the outside. We know that it's on the outside because otherwise there would be parentheses around both and x. There is not, so it is outside. Outside, vertical. This is a vertical change. Looking back at problem two, when a value is >1, which this is, it is a vertical stretch. So this function has a vertical stretch by .

I hope this helps!

fwms@lil_ben06

step-by-step explanation: