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a constant

Q: An exponential function is written as Fx equals a bx where the coefficient a is the base b is positive but not equal to 1 and the exponent x is any number?

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Yes.

the left end of the graph is going in a positive direction and the right end is going in a negative direction.

Yes, but remember that 2 negatives is a positive. so -2 to the 2nd power would be 4, but -2 to the 3rd power would be -8.

positive

When the first derivative of the function is equal to zero and the second derivative is positive.

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any number

positive

"The base of the exponent" doesn't make sense; base and exponent are two different parts of an exponential function. To be an exponential function, the variable must be in the exponent. Assuming the base is positive:* If the base is greater than 1, the function increases. * If the base is 1, you have a constant function. * If the base is less than 1, the function decreases.

No.

The exponential function - if it has a positive exponent - will grow quickly towards positive values of "x". Actually, for small coefficients, it may also grow slowly at first, but it will grow all the time. At first sight, such a function can easily be confused with other growing (and quickly-growing) functions, such as a power function.

If the exponent has the variable of time in it, then it will be either exponential growth (such as compound interest for example), or exponential decay (such as radioactive materials, or a capacitor discharging). If the time constant (coefficient of the time variable) is positive then it is growth, if the time constant is negative, then it is decay.

Not necessarily. If the exponent is not an integer then it is not a polynomial.

The logarithmic function is not defined for zero or negative numbers. Logarithms are the inverse of the exponential function for a positive base. Any exponent of a positive base must be positive. So the range of any exponential function is the positive real line. Consequently the domain of the the inverse function - the logarithm - is the positive real line. That is, logarithms are not defined for zero or negative numbers. (Wait until you get to complex analysis, though!)

true

Yes.

Domain of the logarithm function is the positive real numbers. Domain of exponential function is the real numbers.

Yes, a coefficient of an exponent can be negative. Negative coefficients indicate the opposite direction or opposite effect of positive coefficients in mathematical expressions.