# How do you use end behavior, zeros, y intercepts to sketch the graph of #f(x)=x^3+11x^2+35x+32#?

See explanation

End behavior: the x^3 term is dominant, which means that as x goes out to increasing values of positive x, (or to increasingly NEGATIVE values of negative x), f(x) increases towards positive infinity (or negative infinity), respectively.

y intercept: set x = 0, then f(x) is trivially read off as 32.

Now, this question is under "precalculus", so what follows may be a bit above & beyond. But:

If you've had some calculus, you can take the second derivative of f(x) and do some more analysis, but this may not be totally necessary here. So, to graph this function:

- plot points (-5,7), (-2.3333, -2.47777) (call it 2.5) and (0, 32)
- draw a nice, swoopy curve coming up from negative infinity on the left, topping out at -5,7, then down to -2.333, -2.5, then up to (0, 32), and then on up to positive infinity on the right.

Or, since we live in 2017, you can let your browser graph it:

graph{x^3 + 11x^2 + 35x + 32 [-22.37, 17.63, -8.72, 11.28]}

GOOD LUCK

By signing up, you agree to our Terms of Service and Privacy Policy

- How to understand this question ?
- How do you write a polynomial function of least degree with integral coefficients that has the given zeros 5/3, 1, -1?
- How do you find all the zeros of #x^4 - 4x^3 - 20x^2 + 48x#?
- How many zeroes does #f(x) = x^3 + 3x^2 - x - 3# have?
- Form a polynomial whose zero and degree are given .zeros:_3,multiplicity 1 ;_1,multiplicity 2 ; degree 3 ? Type a polynomial with integer coefficients and a leading coefficient.(simplify your answer)

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7