Question 57120: I am stumped by this one. Use transformations to help graph f(x)=3^(1-x)-4. Also identify domain, range and horizontal asymptote and whether the graph is increasing or decreasing. I know the graph will move 4 to the right. The part that is throwing me off is the exponent. I know -x is a reflection about the x-axis. Please help.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! I am stumped by this one. Use transformations to help graph f(x)=3^(1-x)-4. Also identify domain, range and horizontal asymptote and whether the graph is increasing or decreasing. I know the graph will move 4 to the right. The part that is throwing me off is the exponent. I know -x is a reflection about the x-axis. Please help.
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Sketch the graph y=3^(-x) which is a decreasing function passing
thru (0,1)(1,(1/3)),(2,(1/9) etc; never going below the x axis.
Then y=3^(-x+1) moves that graph "1" to the left.
Then y=3^(-x+1)-4 moves that last graph down 4.
Hope this helps.
Cheers,
Stan H.
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