For a rational function, factorise both the numerator and denominator to help you determine where the vertical asymptotes and x-intercepts are. After that, use a sign diagram to determine whether the function is above or below the x-axis. After that, use the second derivative to determine the concavity of the function at various points. Hope this helps.

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I dont understand how to determine where the graph lies and if it is concave upwards or downwards in a rational function.

For a rational function, factorise both the numerator and denominator to help you determine where the vertical asymptotes and x-intercepts are. After that, use a sign diagram to determine whether the function is above or below the x-axis. After that, use the second derivative to determine the concavity of the function at various points. Hope this helps.