graph and show solution for y = Ix+2I and translated y =- IxI
To graph and show the solution for y = |x + 2|, we can start by understanding the properties of the absolute value function.
The absolute value function (|x|) represents the distance of a number from zero on a number line. It always returns a non-negative value. In this case, we have y = |x + 2|, which means the distance of (x + 2) from zero.
To graph this equation, we can consider different values of x and evaluate y = |x + 2|.
Let's begin with x = -4:
y = |-4 + 2|
y = |-2|
y = 2
So, when x = -4, y = 2.
Similarly, we can choose more values of x and find the corresponding values of y to plot the graph.
x = -3:
y = |-3 + 2|
y = |-1|
y = 1
x = -2:
y = |-2 + 2|
y = |0|
y = 0
x = -1:
y = |-1 + 2|
y = |1|
y = 1
x = 0:
y = |0 + 2|
y = |2|
y = 2
x = 1:
y = |1 + 2|
y = |3|
y = 3
x = 2:
y = |2 + 2|
y = |4|
y = 4
Now, we can plot these points on a graph and connect them to form the graph of y = |x + 2|.
Here is the graph:
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Now let's move on to the next equation, y = -|x|. This equation represents the negative value of |x|.
To graph y = -|x|, we can evaluate different values of x and find the corresponding values of y.
Taking similar values of x as before, we have:
x = -4:
y = -|-4|
y = -4
x = -3:
y = -|-3|
y = -3
x = -2:
y = -|-2|
y = -2
x = -1:
y = -|-1|
y = -1
x = 0:
y = -|0|
y = 0
x = 1:
y = -|1|
y = -1
x = 2:
y = -|2|
y = -2
Plotting these points on a graph and connecting them, we get the graph for y = -|x|:
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So, the graphs of y = |x + 2| and y = -|x| are plotted and shown here.