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2 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.

May 13, 2019

#1
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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.

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.

May 14, 2019