Question
What is the range of the function y = x - 2?
- 2 to + ∞.
- ∞ to - 2.
- ∞ to + ∞.
0 to + ∞.
- 2 to + ∞.
- ∞ to - 2.
- ∞ to + ∞.
0 to + ∞.
Answers
GPT-4o mini
The function \( y = x - 2 \) is a linear function.
As \( x \) can take any real number value from \(-\infty\) to \(+\infty\), the output \( y \) will also cover all real numbers because for each \( x \), there is a corresponding \( y \).
Specifically, as \( x \) approaches \(-\infty\), \( y \) approaches \(-\infty\), and as \( x \) approaches \(+\infty\), \( y \) approaches \(+\infty\).
Thus, the range of the function \( y = x - 2 \) is:
\[
(-\infty, +\infty)
\]
So, the correct answer from your options is:
- ∞ to + ∞.
As \( x \) can take any real number value from \(-\infty\) to \(+\infty\), the output \( y \) will also cover all real numbers because for each \( x \), there is a corresponding \( y \).
Specifically, as \( x \) approaches \(-\infty\), \( y \) approaches \(-\infty\), and as \( x \) approaches \(+\infty\), \( y \) approaches \(+\infty\).
Thus, the range of the function \( y = x - 2 \) is:
\[
(-\infty, +\infty)
\]
So, the correct answer from your options is:
- ∞ to + ∞.