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foreign weamp;#39;re going to use the graph to determine the range of the function y is equal to 1 over 4 X plus five since the graph will show the spread of Y and thatamp;#39;s what the range is all about the the sketch will give you a visual representation of the spread of Y to get the vertical asymptote VA we set 4X plus 5 equal to zero and for X is equal to negative five when we divide both sides by 4 x is equal to negative five fourths negative five fourths and the vertical asymptote will be the vertical line going through negative five fourths now for the horizontal asymptote as X get closer and closer to Infinity where the positive or negative y will be approaching 1 over for x and we know that when the degree of the numerator is less than the degree of the denominator respectively 0 and 1. the limit as 1 over 4 x as X approaches Infinity if x become extremely big one over something extremely big is equal to zero therefore the horizontal asymptote is y equal to