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Let f(x) = |x| + 5

The graph of f(x) is transformed into the graph of g(x) by a translation of 4 units right
and a translation of 3 units down.
What is the equation for g(x)?

User Korayem
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2 Answers

4 votes

Answer:

This function g(x) will have the same shape as f(x) but shifted 4 units to the right and 3 units down.

Explanation:

User Tataelm
by
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4 votes

When a graph is translated to the right by a units, the x-coordinate of each point on the graph increases by a units. So the equation of the transformed function will have x - a in it.

When a graph is translated down by b units, the y-coordinate of each point on the graph decreases by b units. So the equation of the transformed function will have y - b in it.

Given f(x) = |x| + 5 and the graph of f(x) is transformed into the graph of g(x) by a translation of 4 units right and a translation of 3 units down, the equation of the transformed function g(x) will be:

g(x) = f(x - 4) - 3

This is because the x-coordinate increases by 4 units and the y-coordinate decreases by 3 units.

So the equation of g(x) is:

g(x) = |x-4| + 5 - 3

g(x) = |x-4| + 2

This function g(x) will have the same shape as f(x) but shifted 4 units to the right and 3 units down.

User Dmitri Nesteruk
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