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

Jamesx007x7 Mar 2, 2019

#1**+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)^{2 }-3

LagTho Mar 2, 2019

#2**+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

CPhill Mar 2, 2019

#3**+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

#5**+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

CPhill
Mar 2, 2019