Question

How is the log function shifted from the parent function? \(y = \log_{12}(x + 13) - 14\)

A) Shifted 13 units right and 14 units down.

B) Shifted 13 units left and 14 units up.

C) Shifted 13 units right and 14 units up.

D) Shifted 13 units left and 14 units down.

Answer 1

The log function
`\(y = \log_(12)(x + 13) - 14\)` is shifted 13 units left and 14 units down, so the correct option is D.

Step-by-step explanation:

The given logarithmic function
`\(y = \log_(12)(x + 13) - 14\)` can be compared to the standard form of a logarithmic function,
`\(y = \log_b(x)\)`. In this case, the base is 12, and the argument inside the logarithm is
`\(x + 13\)`. The presence of
`\(x + 13\)` means the function is horizontally shifted by 13 units to the left. Additionally, the term
`\(-14\)` outside the logarithm represents a vertical shift downward by 14 units.

To understand this, consider that any addition inside the logarithm causes a horizontal shift, and any addition or subtraction outside the logarithm causes a vertical shift. In this case, the
`\(x + 13\)` inside the logarithm is a horizontal shift, and the
`\(-14\)` outside the logarithm is a vertical shift.

Therefore, the correct interpretation is that the log function is shifted 13 units to the left and 14 units down, aligning with option D.

In conclusion, understanding the effects of the terms inside and outside the logarithmic function helps identify the direction and magnitude of shifts in the graph, leading to the determination that the function is shifted 13 units left and 14 units down.