Question 528566: "graph the function f(x)=4^x. Indicate the y-intercept and the asymptote. Also graph the function g(x)=log_4x. Indicate the x-intercept and the asymptote"
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! "graph the function f(x)=4^x. Indicate the y-intercept and the asymptote. Also graph the function g(x)=log_4x. Indicate the x-intercept and the asymptote
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f(x)=4^x
y-intercept
set x=0
y=4^0=1
note:(all exponential functions, regardless of base, have this same y-intercept, (0,1)
For x>0, y>1 and increases exponentially to approach ∞
For x<0, y<1 and approaches 0, the x-axis, which is the asymptote, y=0
..
g(x)=log4(x)
x-intercept
set y=0
log4(x)=0
log4(1)=0
x=1
note:(all log functions, regardless of base, have this same x-intercept, (1,0)
For x>1, y>0 and increases gradually to approach ∞
For x<1, y<1 and approaches the y-axis, which is the asymptote, x=0
...
Graphing:
For both f(x) and g(x) you have the y and x intercepts and their asymptotes with which you can graph the functions. For f(x), you can easily get third point by plugging in x=1 for f(1)=4, (1,4)
For g(x), plug in the base 4. The log of any base to its base=1, (4,1)
Also, note f(x) and g(x) are inverses of each other.
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