2. Graph the following function using transformations. Be sure to graph all of the stages on one graph. State the domain and range. y= -2 lxl +2

For example, if you were asked to graph y= x^2 + 1 using transformations, you would show the graph of y= x^2 and the graph shifted up 1 unit. Please show all work.

omg I feel so dumb because I don't understand this stuff, could someone please help me?

visit

http://rechneronline.de/function-graphs/

for excellent help with graphs. You can show up to 3 graphs at once, so you can play around with various adjustments and see how they alter the graphs.

There's an instructions button for looking up names of common math functions, like abs(x) for absolute value.

evaluate: (1/121)x

steve....that site isn't working for me!

Nicole....what do I do once I evaluate 1/121x?

Of course, I'll be happy to help you!

To graph the function y = -2 |x| + 2 using transformations, we will first need to understand the transformations involved.

The function y = |x| represents the absolute value of x. It is a V-shaped graph that includes all points where x is positive or negative.

Now, let's break down the given function into stages and explain how each transformation affects the graph:

Stage 1: y = |x|
This is the base graph of the absolute value function. To draw this, plot points for different values of x and y, considering the symmetry around the y-axis. The domain for this stage is all real numbers, and the range is y ≥ 0 (all non-negative numbers).

Stage 2: y = -2 |x|
This transformation scales the graph vertically by a factor of -2. This means that each y-coordinate of the original graph is multiplied by -2. The negative sign also reflects the graph across the x-axis. To visualize this change, multiply the y-values of each point on the Stage 1 graph by -2. The domain and range remain the same.

Stage 3: y = -2 |x| + 2
In this stage, we shift the graph vertically 2 units upward by adding 2 to each y-coordinate. Each point on the Stage 2 graph is shifted upward by 2 units. The domain and range are still the same.

To summarize, the stages of the graphing process are as follows:
1. Start with the graph of y = |x|.
2. Scale the graph vertically by -2 to get y = -2 |x|.
3. Shift the graph 2 units upward to get y = -2 |x| + 2.

By following these steps, you can map out each stage of the graph on a coordinate plane. Remember to label the x and y axes with appropriate scales. Based on the given function, the domain for all stages is all real numbers, and the range is y ≤ 2.

I hope this explanation helps you understand how to graph the given function and the underlying transformations involved. If you have any further questions, feel free to ask!