An html5 applet to explore the properties of logarithmic functions. The parameters $a$, $b$, $c$, $d$ and $B$ included in the definition of a logarithmic function of the form
\[ f(x)= a \log _B(b(x+c))+d \]
may be changed and therefore the graph of function $f$ explored.
Interactive Tutorial - Part 1
set a = 1, b = 1, c = 0, d = 0 and B = 2. Check few points on the graph such as \( \log_2 1 = 0 \), \( \log_2 2 = 1 \), \( \log_2 4 = 2 \). Use zoom in and out if necessary.
Keep the same values for a, b, c and as above and set B = 4. Check few points such as \( \log_4 1 = 0\), \( \log_4 4 = 1 \), \( \log_2 16 = 2 \).
Keep the same values for a, b, c and as above and set B = 0.5 to define function g in part c) above. Check few points such as \( \log_{0.5} 1 = 0 \), \( \log_{0.5} 2 = -1 \), \( \log_{0.5} 4 = -2 \), \( \log_{0.5} 8 = -3 \).
Interactive Tutorial - Part 2
Investigate base B: set a=1, b=1, c=0 and d=0. Set B to values between 0 and 1 and to values greater than one, take note of the different graphs obtained and explain.
Investigate the effects of parameter a (vertical scaling) by setting B = 2, b = 1, c = 0 and d = 0.
Investigate the effects of parameter b (horizontal scaling) by setting a=1, c=0, d = 0 and B = 2.
set B=e, a=1, b=1 and investigate the effects of c (horizontal shifting) and d (vertical translation).
Set B, a, and d to different values and explain how parameters b and c affect the domain of the logarithmic function. Explain analytically.
What parameter(s) affect the x intercept? Is there always an x intercept? Explain analytically.
What parameter(s) affect the y intercept? Is there always a y intercept? Explain analytically.
What parameter(s) affect the vertical asymptote? Explain analytically.