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What else can I help you with?
Does Exponential decay occurs if the base of an exponential function is a positive integer?
Yes.
When an odd function has a negative leading coefficient what happens to the graph?
the left end of the graph is going in a positive direction and the right end is going in a negative direction.
Can the base of an exponential function be a negative number?
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.
The discriminant of the function is?
positive
How can you know that a value is the minimum of a function?
When the first derivative of the function is equal to zero and the second derivative is positive.
An exponential function is written as Fx equals a bx where the coefficient a is a constant the base b is positive but not equal to 1 and the exponent x is?
any number
An exponential function is written as Fx equals a bx where the coefficient a is a constant the base b is but not equal to 1 and the exponent x is any number?
positive
In exponential growth functions the base of the exponent must be greater than 1. How would the function change if the base of the exponent were 1 How would the function change if the base of the expon?
"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.
When rewriting an exponential expression with a negative exponent and a positive base to an expression containing only a positive exponent does the sign of the base change?
No.
How can you identify exponential function from its graph?
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.
Do all exponential functions show growth over time?
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.
If the coefficient of the expression ax is in fraction and the exponent is positive the expression will be a polynomial?
Not necessarily. If the exponent is not an integer then it is not a polynomial.
Why negative numbers don't have logarithim?
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!)
If the coefficient of the expression axn is negative and the exponent is positive will the expression be a polynomial?
true
What happened if the base of exponential function is less than zero?
If the base of an exponential function is less than zero, the function can exhibit complex behavior. Specifically, if the base is a negative number, the function will not be defined for all real numbers, as it will yield complex numbers for non-integer exponents. Consequently, the exponential function may oscillate between positive and negative values, depending on the exponent's parity, which complicates its interpretation in real-world applications. Thus, exponential functions are typically defined with a positive base for meaningful real-valued outputs.
Does Exponential decay occurs if the base of an exponential function is a positive integer?
Yes.
What is the domain of logarithm and exponential function?
Domain of the logarithm function is the positive real numbers. Domain of exponential function is the real numbers.
