Question

test using the lead coefficient to find out if y arrow oo, or
y arrow-oo as x arrow -oo

y=-5x^3+4x^2+6x-7
n is odd -5x^3
an<0 -5x^3
y arrow -oo as x arrow oo

Is this right or do I need to go back and try again??????

Answer 1

As x goes to infinity the only term that matter is -5x^3. As x^3 goes to negative infinity what does is it's sign? If you can't picture it than try separating negative infinity into -1(∞). Then cube it: (-1(∞))^3 which becomes -1(∞)^3 because -1 cubed is still -1. Then what is infinity cubed? Still infinity right? So (-1(∞))^3 is negative infinity. However there's the coefficient to take into account. The negative coefficient will change negative infinity to infinity. So y goes to infinity as x goes to infinity.