The graph of y=f(x) is given above. For what value of x is y=f(x-4) undefined?

Options

A. `-3`
B. `1`
C. `2`
D. `5`

Answer

D

Explanation

Difficult:Easy
Category: Passport to Advanced Math/ Functions
Strategic Advice: Algebraically, a function is undefined when value (or values ) in its domain cannot be evaluted (for example, taking the square root of a negative number or dividing by 0). Graphically, this produces a "hole" (or an asymptote) in the graph.
Getting to the Answer: The graph of f(x), which is show, is undefined at x=1 because there is a hole in the graph, meaning that the function asks where the transformed (shifted) function is undefined. The notation `y=f(x-4)` represents a horizontal shifts of f(x) to the right 4 units (remember, horizontal shifts are always the opposite of how they appear), so imagine moving the hole shown in the graph to the right 4units. The result is (5,2), so the shifted function is undefined at x=5, which is (D).