Mid-Chapter Quiz
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Start by recalling the translations of the parent function, f(x)=x1.
The graph of y2 is the graph of y1 translated 2 units to the left and 4 units down.
Translations of f(x)=x1,x=0 | |
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Vertical Translations | Translation up k units, k>0y=x1+k
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Translation down k units, k>0y=x1−k
| |
Horizontal Translations | Translation right h units, h>0y=x−h1
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Translation left h units, h>0y=x+h1
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Using this table, let's indicate the translation from the graph of the parent function f(x)=x1 to the graph of y1 and y2.
Function | Translation |
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y1=x−11+2 | Translation up 2 units and right 1 unit |
y2=x+11−2 | Translation down 2 units and left 1 unit |
Let's draw the graphs of these two functions on the coordinate plane.
Finally, let's consider a point on the graph of y1. We will see the translation applied to obtain its corresponding point on the graph of y2. For simplicity, let's use the point (0,1).
Therefore, the graph of y2 is the graph of y1 translated 2 units to the left and 4 units down.