Domain and Range of Logarithmic Functions
Move the sliders to transform the parent logarithmic function f(x) = ln x
into the function f(x) = a*ln (x - h) + k.
Write the domain, range and the equation of the vertical asymptote for each of the examples that follow.
1. f(x) = 2*ln(x + 3)
2. f(x) = 0.4*ln(x-3) - 1
3. f(x) = -3*ln(x-1) + 4
4. f(x) = -0.5*log x - 2
Journal Entry:
Describe how the values of a, h, and k can be used to find the domain and range of a logarithmic function in the form f(x) = a ln (x - h) + k.
Compare the domain and range of f(x) = a ln (x - h) + k. to the domain and range of its parent function
f(x) = ln x. Which of the values a, h, or k have a role in determining the domain and range? Why? Use specific examples to support your claims.