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Answered

If the graph of y = |x| is translated so that the point (1, 1) is moved to (4, 1), what is the equation of the new graph?


y = |x - 3|

y = |x| - 3

y = |x + 3|

y = |x| + 3

Verified Answer :

meerkat18

This may be done by plugging in the value of the coordinates of the point (4, 1) in the equation. It may be seen that to get an answer for y of 1, x should be subtracted by 3. We can choice either from first and second choice; however, it is x that is being translated so, -3 should appear inside the absolute value sign.

calculista

we know that

the point \((1, 1)\) is moved to \((4, 1)\)

so

the rule of the translation is

\((x,y)---------> (x+3,y)\)

that means

the translation is \(3\) units to the right

therefore

the answer is

the equation of the new graph is

\(y=\left|x-3\right|\)

see the attached figure to better understand the problem

View image calculista

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