Question

Consider the following two functions.

Original: f(x)=|x| +1

Final: f(x)=12|x| +12

Which option best describes the change from the original to the final function?

Option #1: a vertical stretch

Option #2: a vertical compression

Option #3: no change

(1 point)
The change is best described by Option #
.

Answer 1

To analyze the change from the original function \( f(x) = |x| + 1 \) to the final function \( f(x) = 12|x| + 12 \), we can look at how each component of the function has been modified.

1. The original function has \( |x| \) and adds 1 to it, which means that the whole function is shifted upwards by 1 unit.
2. The final function has \( 12|x| \), which means that it stretches the \( |x| \) component vertically by a factor of 12, as it scales the value of \( |x| \) by 12.
3. Additionally, it also adds 12 to the entire function, which shifts the whole function upwards by another 12 units.

Since we are specifically looking at the change from the original to the final function, we must focus on the stretching effect due to the factor of 12 applied to \( |x| \).

Thus, the change from the original function to the final function is best described as **a vertical stretch**.

So, the answer is: **Option #1: a vertical stretch.**