document.write( "Question 458507: I can't find the domain and range of f(x)=-2(0.5)^x +1 \n" ); document.write( "

Algebra.Com's Answer #315531 by lwsshak3(11628) $\"\"$ $\"About$

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

\n" );