please help me with this problem x^4/x^2+2?

Question

i need graph this. please show me the steps

denominator (x^2+2)
with out calculator

Answer 1

For large values of x, x^4/(x^2+2) ≈ x^4/(x^2) (the value of x^2 gets much bigger than 2, so the 2 can be ignored) So for large values of x (x>10, say) this will look like the graph of x^2, a parabola. This is true for both positive and negative x values. For very small values of x, x^2 is small compared to 2, so it can be ignored and the equation looks like (x^4)/2; but for x small, x^4 is very small and the function is flat; this is in the region |x| < .1 The remaining region .1 < |x| < 10 can be sketched in with the help of a few key points like x = +/-1 (giving a vaue of 1/3), and x = +/- 2 giving a value of 16/6, etc.

Answer 2

is the denominator of the fraction/ expression X^2 + 2, or just X^2?

if you need to graph it, can't you just input the expression exactly as is into the calculator (TI-83, 85, whatever)? Or do you mean by hand?