Answer:
[tex]y=\left|\dfrac{1}{2}x-\dfrac{5}{2}\right|+3[/tex]
Step-by-step explanation:
Given equation:
[tex]y=\left|\dfrac{1}{2}x-2\right|+3[/tex]
Translation
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
When translating a graph to the right, subtract the number of units from the x variable.
Translating the given graph one unit to the right:
[tex]f(x-1) \implies y=\left|\dfrac{1}{2}(x-1)-2\right|+3[/tex]
Simplifying:
[tex]\implies y=\left|\dfrac{1}{2}(x-1)-2\right|+3[/tex]
[tex]\implies y=\left|\dfrac{1}{2}x-\dfrac{1}{2}-2\right|+3[/tex]
[tex]\implies y=\left|\dfrac{1}{2}x-\dfrac{5}{2}\right|+3[/tex]
Learn more about graph transformations here:
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