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 united to the left . shift 4 units down

Answer 1

• f(x + 5) = |x + 5|, represents the requested change of 5 units to the left,

• f(x) - 4 = |x| - 4, represents the requested change of 4 units down.

Explanation:

The following rules will permit you to predict the equation of a new function after applying changes, especifically translations, that shift the graph of the parent function in the vertical direction (upward or downward) and in the horizontal direction (left or right).

• Horizontal shifts:

Let the parent function be f(x) and k a positive parameter, then f (x + k) represents a horizontal shift of k units to the left, and f (x - k) represents a horizontal shift k units to the right.

• Vertical shifts:

Let, again, the parent function be f(x) and, now, h a positive parameter, then f(x) + h represents a vertical shift of h units to upward, and f(x - h) represents a vertical shift of h units downward.

• Combining the two previous rules, you get that f (x + k) + h, represents a vertical shift h units upward if h is positive (h units downward if h is negative), and a horizontal shift k units to the left if k is positive (k units to the right if k negative)

Hence, since the parent function is f(x) = |x|

• f(x + 5) = |x + 5|, represents the requested change of 5 units to the left,

• f(x) - 4 = |x| - 4, represents the requested change of 4 units down.

Furthermore:

• f(x + 5) - 4 = |x + 5| - 4, represents a combined shift 5 units to the left and 4 units down.