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Question
Which of the following is the graph of f(2$)= |x| reflected on the x-axis, translated 3units left, 4 units up, and dilated by a factor of 4?
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Answer
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Step 1:
First, let's find the equation of the reflected function on the x-axis, which is $-f(x) = -|x|$.
Step 2:
The equation becomes $-f(x - 3) = -|x - 3|$.
Next, we translate the function 3 units to the left.
Step 3:
The equation becomes $-f(x - 3) + 4 = -|x - 3| + 4$.
Then, we translate the function 4 units up.
Step 4:
The equation becomes $-4f(x - 3) + 16 = -4|x - 3| + 16$.
Finally, we dilate the function by a factor of 4.
Final Answer
The graph of $f(x) = |x|$ reflected on the x-axis, translated 3 units left, 4 units up, and dilated by a factor of 4 is represented by the equation $- 4f(x - 3) + 16 = - 4|x - 3| + 1$.
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