To determine which of the given equations is not exponential, we need to understand the property that defines an exponential function. An exponential function generally has the form [tex]\(y = a^x\)[/tex], where [tex]\(a\)[/tex] is a constant base and [tex]\(x\)[/tex] is the exponent.
1. For the equation [tex]\( y = 1^x \)[/tex]:
- The base is [tex]\(1\)[/tex].
- Any non-zero number raised to the power of [tex]\(x\)[/tex] means the output is [tex]\(1\)[/tex].
- Therefore, [tex]\(1^x\)[/tex] is a constant function and does not exhibit exponential growth or decay. It just remains [tex]\(1\)[/tex] regardless of the value of [tex]\(x\)[/tex].
2. For the equation [tex]\( y = (1/2)^x \)[/tex]:
- The base is [tex]\(1/2\)[/tex], which is a positive number less than [tex]\(1\)[/tex].
- This function represents exponential decay because as [tex]\(x\)[/tex] increases, [tex]\((1/2)^x\)[/tex] gets smaller and approaches zero.
- Therefore, this is an exponential function.
3. For the equation [tex]\( y = -2^x \)[/tex]:
- The base here is [tex]\(-2\)[/tex]. However, if we consider the base as [tex]\(2\)[/tex], then multiply by [tex]\(-1\)[/tex], the function can still be considered within the exponential form but with a negative association to it.
- Strictly speaking, if we see [tex]\(2^x\)[/tex] as the exponential part, adding a negative sign makes it a reflection along the x-axis. It still shows the exponential nature of growth or decay.
- Therefore, this could still be considered an exponential function depending on interpretation.
Given the above analysis, we conclude that:
The equation [tex]\( y = 1^x \)[/tex] is not exponential because it doesn’t change regardless of the value of [tex]\( x \)[/tex]. It is a constant function.
