Question

If you apply the changes below to the absolute value parent function, f(x) = x,

what is the equation of the new function?
• Shift 5 units right.
• Shift 7 units down.
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A. g(x) = |x-71 +5
B. g(x)= x + 51-7
C. g(x) = |x-71 - 5
D. g(x)= |x-51-7

Answer 1

To shift the absolute value parent function, f(x) = |x|, 5 units to the right and 7 units down, we need to make the following changes to the equation:

To shift the absolute value parent function, f(x) = |x|, 5 units to the right and 7 units down, we need to make the following changes to the equation:

For the horizontal shift of 5 units to the right, we replace x with (x + 5).

For the vertical shift of 7 units down, we subtract 7 from the entire equation.

Applying these changes, the equation of the new function, g(x), would be:

g(x) = |(x + 5)| - 7

Therefore, the correct option is:

D. g(x) = |x + 5| - 7