document.write( "Question 62633: What is the domain and range of the following function. y=-2^x+1 \n" ); document.write( "

Algebra.Com's Answer #43443 by funmath(2933) $\"\"$ $\"About$

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What is the domain and range of the following function. $\"y=-2%5Ex%2B1\"$
\n" ); document.write( "If the exponent is supposed to be x+1 instead of x, let me know and I'll edit this.
\n" ); document.write( "The domain of exponential functions is ALL REAL NUMBERS because there are no restrictions on the value of x.
\n" ); document.write( "Interval Notation: (-infinity, infinity)
\n" ); document.write( "Set builder Notation: {x|x=R}
\n" ); document.write( ":
\n" ); document.write( "The range, you have to think about. There is no power that you can raise something to that will make it =0 or change its sign. 2^x will get close to, but never be 0. The - infront tells you that the function declines exponentially. The +1 tells us that the highest this function will get close to is 1. Therefore the range is:
\n" ); document.write( "Interval notation: (1,-infinity)
\n" ); document.write( "Set Builder Notation: {y|y<1}
\n" ); document.write( ":
\n" ); document.write( "If you're allowed to use a graphing calculator, look at the graph:
\n" ); document.write( " $\"graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C-2%5Ex%2B1%29\"$
\n" ); document.write( "It goes forever left and right, therefore the domain is all real numbers.
\n" ); document.write( "The highest it approaches is y=1 and it shoots down to -infinity therefore the range is {y|y<1}
\n" ); document.write( "Happy Calculating!!! \n" ); document.write( "

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