Question 458507
I can't find the domain and range of f(x)=-2(0.5)^x +1
..
f(x)=-2(0.5)^x +1
rewrite equation
f(x)=-2(1/2)^x+1
f(x)=-2(1/2^x)+1
First, look at the basic exponential function,1/2^x
You can see at x=0, the function is=1
As x>0 the denominator 2^x becomes larger and the function becomes smaller, making the x-axis a horizontal asymptote.
As x<0 the denominator 2^-x becomes smaller and the function becomes larger to infinity.
The +1 in the function bumps the entire curve one unit up so the horizontal asymptote is at y=1.
The coefficient, makes the curve a little steeper and you can almost ignore it .
The last important factor is the negative sign which means the entire curve must be reflected about the x-axis.
ans:
Domain:(-&#8734;,&#8734;)
Range: (-&#8734;,-1)