



 
Hi Lyric, It really helps to have in your head the shape of the graph of a few simple functions and be able to build in them. For example I know that y = x is the straight line through the origin at a 45^{o} angle an y = x^{2} is a parabola that open upwards with its vertex at the origin. I also know what the graph of y = 1/x looks like. y = 1/x Your function y = 4 x^{4} = 4/x^{4} is similar in some ways, one being that the variable appears in the denominator. The 4 in the numerator is of little consequence as far as the shape of the graph is concerned, it just stretches the graph in the ydirection by a factor of 4. The fact that the denominator is x^{4} rather than x has a significant effect on the graph. If x is negative then y = 1/x is also negative so a piece of the graph lies below the Xaxis. If x is either positive or negative y = 4/x^{4} is positive and hence the graph of y = 4/x^{4} lies entirely above the Xaxis. Can you see how to modify the graph of y = 1/x to obtain the graph of y = 4/x^{4}? Penny  


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