Which statement correctly describes the end behavior of f(x)=−9x4+3x3+3x2−1?
As x→∞, f(x)→∞, and as x→−∞, f(x)→−∞.
As x→∞, f(x)→−∞, and as x→−∞, f(x)→∞.
As x→∞, f(x)→∞, and as x→−∞, f(x)→∞.
As x→∞, f(x)→−∞, and as x→−∞, f(x)→−∞.
is it As x→∞, f(x)→−∞, and as x→−∞, f(x)→∞.
No. the predominate term, x^4 is even, so it predominates at end.
x approaches +- inf, f(x) approaches negative inf
Nicely stated Bob : )
so would it be As x→∞, f(x)→−∞, and as x→−∞, f(x)→−∞.
Think about the shape of an x^4 graph...
Now think about the shape of an -x^4 graph...
(hint: the x^4 looks a wee bit like a w... while the -x^4 looks a wee bit like a w reflected over the x-axis (so a flipped w)...
A regular w has both ends heading towards the sky (positive infinity)... while if you flip the w over (it becomes an m) and you see that both ends are now heading towards negative infinity!
Yes, the correct statement describing the end behavior of f(x)=-9x^4+3x^3+3x^2-1 is: "As x→∞, f(x)→−∞, and as x→−∞, f(x)→∞."
To determine the end behavior, you can analyze the leading term of the function, which in this case is -9x^4. The exponent of x is even, and the leading coefficient is negative. This indicates that as x approaches positive infinity, the function will tend towards negative infinity. Similarly, as x approaches negative infinity, the function will tend towards positive infinity.