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Can someone please help me with these problems and explain how the solution is found?

 Mar 2, 2019
 #1
avatar+234 
+2

I can't help with the second part, for I am not to good at functions. In the first part, you have three equations saying, if x is between these two numbers, then this is the equation. So it tells us that x = -3, so we know that it's the second equation. So just use a graphing calculator to graph the function f(-3) = (x+2)-3

 Mar 2, 2019
 #2
avatar+102948 
+3

1.  Here's the graph : https://www.desmos.com/calculator/sr1qh8cxfs

 

f(x) = - 3

We want to know  what values of x produce a y value of - 3

 

The graph shows three  points where this is true  (-4.5, - 3)  ( -2, - 3)  and (12, - 3)

 

2.   The parent graph is   f(x) = l x l      ( absolute value graph )

It wil have a "V" shape

 

f(x)  = -3 l x + 1 l - 2

 

The "- " reflects the graph over the x axis

The "3"  vertically stretches the graph by a factor of 3

"x + 1"  indicates that the graph is shifted to the left by 1 unit

The " -2 "  shifts the graph downward by 2 units

 

 

cool coolcool

 Mar 2, 2019
 #3
avatar+17 
+1

Thanks for the answer!!! Is there any direction you can point me to learn more about finding the answer when they ask for the value of f(x)=-3 i would really like to learn that

Jamesx007x7  Mar 2, 2019
 #4
avatar+234 
+2

Ok nvm CPhill got it. Sorry for any confusion I might have caused.

LagTho  Mar 2, 2019
edited by LagTho  Mar 2, 2019
 #5
avatar+102948 
+1

Set each function to -3   and see if the x value you find falls within the domain of the given function

 

For instance

 

Set 

 

2x + 6 =  - 3      subtract  6 from both sides

 

2x = - 9         divide both sides by 2

 

x = -9/2  =  -4.5

 

Note that this value is  within the function's domain of   x ≤  - 4

 

Try this with the other two functions and see that you will find solutions that fall within their domains as well

 

If you need help....let me know

 

 

cool cool cool

CPhill  Mar 2, 2019

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