\(y=a^x\), where a is greater than zero but not equal to 1 and x is an exponent
This is an exponential function where the base is a and the exponent is x. As x increases, the value of y increases exponentially. When a is greater than 1, the function will have a vertical asymptote at x=0 and will approach y=0 as x approaches negative infinity. When a is between 0 and 1, the function will approach y=0 as x approaches positive infinity and will have a horizontal asymptote at y=0. If a is less than 0, the function will be undefined for all real values of x.
If a is less than 0, the function will be undefined for all real values of x.
This is not always true.
(-4)^2 = 16
(-2.378)^-3 = -0.07436...
The statement is "true" only if you define a^x = e^(x ln(a))
The equation \(y=a^x\) represents an exponential function. In this function, the base (a) is a positive number greater than zero, but not equal to 1, and x is the exponent.
To evaluate this function and find the value of y for a given x and a, you need to raise the base (a) to the power of the exponent (x). Here's how you can do that:
1. Take the value of a.
2. Raise it to the power of x.
3. The result is the value of y.
For example, let's say we have \(y=2^3\). In this case, a = 2 and x = 3. To find y, we raise 2 to the power of 3:
\(y = 2^3 = 2\times2\times2 = 8\)
So, when a = 2 and x = 3, the value of y is 8.
Similarly, if we have \(y=5^{2}\), a = 5 and x = 2. To find y, we raise 5 to the power of 2:
\(y = 5^2 = 5\times5 = 25\)
In this case, when a = 5 and x = 2, the value of y is 25.
You can follow these steps to evaluate any exponential function of the form \(y=a^x\) where a is greater than zero but not equal to 1, and x is the exponent.