Hi! I've been struggling over this for weeks now. It's long overdue and every time I try to work on it, I can't seem to get it working. Were allowed to use desmos on the graphing part but now I dont understand anything other than my points on graph that were filled out thanks to desmos. So, I have no clue how to go about the "evaluate", "explain" and "use" questions. I appreciate any help possible. I need this is asap.

Guest May 13, 2019

#1**+3 **

**1.**

**Graph the function \(f(x)=\begin{cases} x+6 & x\leq -4 \\ (x+2)^2-3 & -4< x\leq 1\\ -|x-4|+5 & x>1 \end{cases} \)**

Here's the graph of the function on desmos:

https://www.desmos.com/calculator/de2hbs4llz

Notice that the way to specify an interval on desmos is by putting it inside { }'s at the end of the equation.

**What is the value f(x) = -3 ?**

I think this is asking what x values make f(x) be -3.

On the graph, we can look for values of x that make f(x) be -3 .

There are three different x values that make f(x) be -3.

f( -4.5 ) = -3

f( -2 ) = -3

f( 12 ) = -3

**Explain how you would graph something like this without using Desmos:**

You could plot points, making sure to plot points within each of the three intervals, and using the knowledge that the first piece is a part of a line, the second piece is a part of a parabola, and the fourth piece is a part of an absolute value graph.

hectictar May 14, 2019

#2**+3 **

**2.**

**What is the parent function and what general shape does the parent function have?**

The parent function is f(x) = |x|

Its general shape is a "V" shape.

**Explain all of the parameters and what they do to change the graph.**

The graph of f(x) = -3|x + 1| - 2 is the graph of f(x) = |x|

shifted to the left by 1 unit,

stretched vertically by a factor of 3,

flipped over the x-axis,

and shifted down by 2 units.

1 is added to x, which shifts the graph to the left by 1 unit.

3 is multiplied by |x + 1| which stretches the graph vertically by a factor of 3 .

-1 is multiplied by 3|x + 1| which flips the graph over the x-axis.

-2 is added to -3|x + 1| which shifts the graph down by 2 units.

hectictar May 14, 2019