how to determine a polynomial function from a graph

( 2 0,4 x ) x=2. ( x )=2 3 x1 the graph passes through the axis linearly, suggesting the corresponding factors of the polynomial will be linear. , and a root of multiplicity 1 at 4 How can we find the degree of the polynomial? (While the theorem is intuitive, the proof is actually quite complicated and requires higher mathematics.) The graph appears below. x=3,2, Continue with Recommended Cookies. g(x)= (x+1) Step 1. x The sign of the lead. g( x=4. t+1 x= )=0. f(x)= A right circular cone has a radius of The graph touches the x-axis, so the multiplicity of the zero must be even. has horizontal intercepts at ( x1 \end{array} \). +4 ), f(x)=x( The zero of Let 4 x x=3,2, 0,7 Do all polynomial functions have as their domain all real numbers? 3 6 Factor it and set each factor to zero. The exponent on this factor is \( 3\) which is an odd number. x g( The Factor Theorem For a polynomial f, if f(c) = 0 then x-c is a factor of f. Conversely, if x-c is a factor of f, then f(c) = 0. f(x) also decreases without bound; as At \(x=3\), the factor is squared, indicating a multiplicity of 2. (x4). increases without bound and will either rise or fall as Over which intervals is the revenue for the company increasing? Sometimes we may not be able to tell the exact power of the factor, just that it is odd or even. The last zero occurs at x Starting from the left, the first zero occurs at \(x=3\). have opposite signs, then there exists at least one value n This happened around the time that math turned from lots of numbers to lots of letters! consent of Rice University. Direct link to 999988024's post Hi, How do I describe an , Posted 3 years ago. w 202w 6 f is a polynomial function, the values of I need so much help with this. ) x this polynomial function. k( The graph curves up from left to right passing through the negative x-axis side, curving down through the origin, and curving back up through the positive x-axis. Step 2. x 2 ) =0. 0