Question

Which of the following is the value of a when the function f(x) = 3|x + a| is written in the standard form of an absolute value function?

a) -1
b) -3
c) 1
d) 3

Answer 1

The function f(x) = 3|x + a| is already in the standard form of an absolute value function with a = 0, as there is no need for horizontal translation. Therefore, none of the provided options is the correct value of a.

Step-by-step explanation:

The question asks for the value of a when the function f(x) = 3|x + a| is expressed in the standard form of an absolute value function. The standard form for absolute value functions is typically written as f(x) = k| x - h | + c where (h, c) is the vertex of the graph of the absolute value function and k denotes the vertical stretch or compression. In order to identify the value of a, the provided function f(x) = 3| x + a | must match the standard form. Since the absolute value expression is |x + a|, the function is a horizontal translation a units to the left of the origin if 'a' is positive and to the right if 'a' is negative. However, in this case, no translation is needed to express it in standard form, which implies that a is 0. Therefore, none of the provided options a) -1, b) -3, c) 1, or d) 3 is correct. The function is already in standard form with a equal to 0.