Question

Given the parent function f(x) = x, write the equation showing that the following transformations have been applied: reflection across the x-axis, a shift to the left 3 units, and a shift down 4 units

Answer 1

To reflect the parent function f(x) = x across the x-axis, shift it to the left by 3 units, and shift it down by 4 units, the transformed equation is g(x) = -x - 7.

Step-by-step explanation:

The question involves applying a series of transformations to the parent function f(x) = x. We need to reflect the function across the x-axis, shift it to the left by 3 units, and then shift it down by 4 units. To reflect a function across the x-axis, we multiply the function by -1. To shift the function to the left by 3 units, we replace x with x + 3. Lastly, to shift the function down by 4 units, we subtract 4 from the function.

So the transformed equation becomes: g(x) = -f(x + 3) - 4.

Substituting the parent function f(x) = x into the transformation gives us the final equation: g(x) = -(x + 3) - 4 = -x - 3 - 4 = -x - 7.