Question
What is the range of the function g(x) = |x – 12| – 2?
{y | y > –2}
{y | y > –2}
{y | y > 12}
{y | y > 12}
{y | y > –2}
{y | y > –2}
{y | y > 12}
{y | y > 12}
Answers
GPT-4o mini
To find the range of the function \( g(x) = |x - 12| - 2 \), we first need to analyze the expression \( |x - 12| \).
The absolute value function \( |x - 12| \) produces values that are always non-negative, meaning that \( |x - 12| \geq 0 \). Therefore, subtracting 2 from \( |x - 12| \) gives us:
\[
g(x) = |x - 12| - 2 \geq 0 - 2 = -2
\]
This means that the minimum value of \( g(x) \) is \(-2\). It occurs when \( |x - 12| = 0 \), which happens when \( x = 12 \).
As \( x \) moves away from 12 in either direction (either becoming larger or smaller than 12), the value of \( |x - 12| \) increases, causing \( g(x) \) to increase as well. Thus, \( g(x) \) can take on any value greater than \(-2\).
Thus, the range of the function \( g(x) \) is:
\[
\{y | y > -2\}
\]
Among your options, the correct answer is:
**{y | y > –2}**
The absolute value function \( |x - 12| \) produces values that are always non-negative, meaning that \( |x - 12| \geq 0 \). Therefore, subtracting 2 from \( |x - 12| \) gives us:
\[
g(x) = |x - 12| - 2 \geq 0 - 2 = -2
\]
This means that the minimum value of \( g(x) \) is \(-2\). It occurs when \( |x - 12| = 0 \), which happens when \( x = 12 \).
As \( x \) moves away from 12 in either direction (either becoming larger or smaller than 12), the value of \( |x - 12| \) increases, causing \( g(x) \) to increase as well. Thus, \( g(x) \) can take on any value greater than \(-2\).
Thus, the range of the function \( g(x) \) is:
\[
\{y | y > -2\}
\]
Among your options, the correct answer is:
**{y | y > –2}**