polynomials + exponential and logarithmic function

x²+Bx+C roots α,β

• B = - (α+β)

• C = αβ

how does the base of an exponential functions affect the graph of the function

• when base is bigger than 1 → exponential growth + bigger base = steeper function e.g 4 to the power of x is steeper than 2 to the power of x

• when base is positive but smaller than 1 → exponential decay (when power is negative it is also exponential decay)

y intercept of a exponential function

• = 1 + b

• e.g function (4 to the power of x) + 1 has a y-intercept of 2

what is the equation of the asymptote for an exponential function

• y = b

• e.g function (4 to the power of x) + 1 has an asymptote at y = 2

• e.g function 2 to the power of x has an asymptote at y=0

how does a base of a log affect its graph as a function

• base is bigger than 1 → exponential growth + bigger base = steeper graph

• 0 < base < 1 → exponential decay

• log base b and log base b to the power of -1 are symmetrical over the x-axis

domain + range of logarithmic functions

• range = any real number

• domain e.g log x = x >0

y and x intercept of log functions

• no y-intercept

• x-intercept = (1,0)

relationship between exponential + log functions

• f(x) = a to the power of x

• f to the -1 (x) = log base a (x)