Question

1. List 10 facts about exponential functions.

2. List 10 facts about logarithm functions.

Answer 1

10 facts about exponential functions:

1) Parent exponential function f(x) = b^{​​​​​​x} always has a horizontal asymptote at y = 0, except when b = 1. 2) Domain of exponential function is (–∞,∞). 3) It does not have negative base. 4) When you multiply monomials with exponents, you add the exponents. 5) When you have multiple factors inside parentheses raised to a power, you raise every single term to that power. 6) A number with a negative exponent is the reciprocal of the number to the corresponding positive exponent. 7) When graphing an exponential function, remember that the graph of an exponential function whose base number is greater than 1 always increases (or rises) as it moves to the right; as the graph moves to the left, it always approaches 0 but never actually get there. 8) The argument of the exponential function can be any real or complex number or even an entirely different kind of mathematical object. 9) Its inverse function is the natural logarithm. 10) The natural exponential function is e^{​​​​​​x}.

10 facts about logarithm function:

1) The log of a power is the power times the log. 2) Zero and One Laws

log_{​​​​b}(b)=1 (Because b^{​​​​​​1}=b)

log_{​​​​b}(1)=0 (Because b^{​​​​​​0}=1). 3) The log of a product (quotient) is the sum (difference) of the logs. log_{​​​​b}(xy)=log_{​​​​b}(x)+log_{​​​​b}(y) log_​b(x/y)= log_{​​​​b}(x)–log_b(y) 4) Natural log is log base e. log_{​​​​e}(x) = ln(x) 5) Changing bases: log_​a(x) = log_{​​​​b}(x)/ log_{​​​​b}(a). 6) It is inverse of exponential function. 7)  A logarithm of base 10 is called a common log. 8) For any base, the x-intercept is 1. 9) The graph is below the x-axis -- the logarithm is negative -- for

0 < x < 1. 10) The range of the function is all real numbers.