Question

Input the missing values in the function for the graph. Y = |x - [?]| + [?]

a) 0, x
b) x, 0
c) x, x
d) 0, 0

Answer 1

The correct values to fill in the absolute value function y = |x - [?]| + [?] are 0 for the horizontal shift and 0 for the vertical shift, making the standard absolute value function y = |x|. Therefore, the answer is d) 0, 0.

Step-by-step explanation:

The question asks to fill in the missing values in the absolute value function y = |x - [?]| + [?]. The brackets are placeholders for the missing values.

Looking at options a) through d), we want to determine which pair of constants would make the equation a valid representation for a graph when plugged into the missing spots. The placeholder first represents the horizontal shift of the graph and the second represents the vertical shift of the absolute value graph.

Options Analysis:

• a) 0, x: This would result in y = |x - 0| + x, which is not a standard absolute value function.
• b) x, 0: This would yield y = |x - x| + 0, which simplifies to y = 0, a horizontal line, not an absolute value graph.
• c) x, x: This results in y = |x - x| + x which simplifies to y = x, not an absolute value graph.
• d) 0, 0: This is the correct answer, yielding y = |x - 0| + 0 which simplifies to y = |x|, which is the standard form for an absolute value graph.

Therefore, the correct values to input into the function are 0 for the horizontal shift and 0 for the vertical shift, making the answer d) 0, 0.