Let's carefully examine each option to determine which equation represents a function.
1. Option A: [tex]\(x = 13\)[/tex]
- This equation represents a vertical line where [tex]\(x\)[/tex] is always 13, regardless of [tex]\(y\)[/tex].
- A vertical line does not pass the vertical line test: for each [tex]\(x\)[/tex], there might be multiple [tex]\(y\)[/tex] values.
- Therefore, [tex]\(x = 13\)[/tex] is not a function.
2. Option B: [tex]\(x - 12 = 34\)[/tex]
- Rearranging the equation, we get [tex]\(x = 46\)[/tex].
- This represents another vertical line where [tex]\(x\)[/tex] is always 46.
- A vertical line does not pass the vertical line test.
- Therefore, [tex]\(x - 12 = 34\)[/tex] is not a function.
3. Option C: [tex]\(2y = -12\)[/tex]
- Solving for [tex]\(y\)[/tex], we get [tex]\(y = -6\)[/tex].
- This represents a horizontal line where [tex]\(y\)[/tex] is always -6.
- A horizontal line passes the vertical line test: for each [tex]\(x\)[/tex], there is exactly one [tex]\(y\)[/tex] value.
- Therefore, [tex]\(2y = -12\)[/tex] is a function.
4. Option D: [tex]\(2x - 4x = 7\)[/tex]
- Simplifying the equation, we get [tex]\(-2x = 7\)[/tex], and then [tex]\(x = -\frac{7}{2}\)[/tex].
- This represents a vertical line where [tex]\(x\)[/tex] is always [tex]\(-\frac{7}{2}\)[/tex].
- A vertical line does not pass the vertical line test.
- Therefore, [tex]\(2x - 4x = 7\)[/tex] is not a function.
5. Option E: [tex]\(\frac{\pi}{2} = 15\)[/tex]
- This is an incorrect statement as [tex]\(\frac{\pi}{2}\)[/tex] is approximately 1.57, not 15.
- This does not represent a function or even a valid equation.
After analyzing all the options, the correct equation that represents a function is:
Option C: [tex]\(2y = -12\)[/tex]
