Question
The g(x)=8vert x-15vert -30 is a transformation of the parent function p(x)=vert xvert Which of the following correctly describes the transformation of function p that generates function g? A p is translated 15 units right, then has a vertical stretch by a factor of 8 and then is translated 30 units down. B p is translated 15 units left, then has a vertical stretch by a factor of 8 and then is translated 30 units up. C p is translated 30 units down, then has a vertical shrink by a factor of 8, and then is translated 15 units right. D p has a vertical shrink by a factor of 8, then is trar lated 15 units down, and then is translated 30 units left. translated
Solution
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Resposta
To determine the transformation of the parent function
that generates the function
, we need to analyze the given function.The given function is
.Comparing this with the parent function
, we can see that the function
has the following transformations:1. The absolute value function is shifted 15 units to the right by replacing
with
.2. The absolute value function is vertically stretched by a factor of 8 by multiplying the absolute value by 8.3. The function is shifted 30 units down by subtracting 30 from the function.Therefore, the correct answer is:A.
is translated 15 units right, then has a vertical stretch by a factor of 8 and then is translated 30 units down.