Math CentralQuandaries & Queries


Question from lyric, a student:

tell whether the graph opens up or down. write an equation of the axis of symmetry

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 45o angle an y = x2 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

y = 1/x

Your function y = 4 x-4 = 4/x4 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 y-direction by a factor of 4. The fact that the denominator is x4 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 X-axis. If x is either positive or negative y = 4/x4 is positive and hence the graph of y = 4/x4 lies entirely above the X-axis.

Can you see how to modify the graph of y = 1/x to obtain the graph of y = 4/x4?


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