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### Translation and Shift

You can alter functions that incorporate absolute values so that you move your graph along the x or y axis. This activity is known as translation. To see how this is so, consider again the equation used to generate a graph that is symmetrical to the y axis (see Figure 7.4):

f (x) = |x|

If you add a value to the absolute value of x, you can move the resulting graph up or down the y axis. A positive value moves it up. A negative value moves it down. To see how this is so, consider an equation that involves translating the graph up by 4:

y = 4 + |x|

Even if x is a negative value, the absolute value sign makes it positive. For this reason, adding 4 to the value of x always increases the corresponding y value by 4. As Figure ...

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