Question

Function (g) can be thought of as a translated (shifted) version of \(f(x) = |x|\).

A) (g(x) = |x - 3| - 1)

B) (g(x) = |x + 3| + 1)

C) (g(x) = |x + 3| - 1)

D) (g(x) = |x - 3| + 1)
a. A

b. B

c. C

d. D

Answer 1

The correct option that represents the absolute function shifted 3 units to the right and 1 unit down is option A: g(x) = |x - 3| - 1. This involves a horizontal shift to the right and a vertical shift downwards.

Step-by-step explanation:

The student's question relates to the translations of the absolute value function f(x) = |x|. In the context of algebra, a translation of a function involves shifting the graph of the function horizontally and/or vertically without changing its shape.

If you have a function f(x), then f(x - d) represents a shift to the right by d units, while f(x + d) shifts the function to the left by d units. Likewise, adding a constant to the function (f(x) + c) shifts it vertically up by c units, whereas subtracting a constant (f(x) - c) shifts it down by c units.

In this case, we are comparing the given options to determine which one represents the absolute value function shifted 3 units to the right and 1 unit down.

The correct transformation would be g(x) = |x - 3| - 1, which corresponds to option A, because the x coordinate is reduced by 3 (shifting the function to the right), and the entire function is decreased by 1 (shifting it downward).