How do you graph an inequalities?
How to Graph a Linear Inequality
- Rearrange the equation so “y” is on the left and everything else on the right.
- Plot the “y=” line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)
- Shade above the line for a “greater than” (y> or y≥) or below the line for a “less than” (y< or y≤).
What is a polynomial inequality?
A polynomial inequality is an inequality where both sides of the inequality are polynomials. For example, x 3 ≥ x 4 x^3 \ge x^4 x3≥x4 is a polynomial inequality which is satisfied if and only if. 0 \le x \le 1. 0≤x≤1. These inequalities can give insight into the behavior of polynomials.
Which statement is the first step to solving a polynomial inequality?
The first step in solving a polynomial inequality is to find the polynomial’s zeroes (its x-intercepts). Between any two consecutive zeroes, the polynomial will be either positive or negative.
How do you graph inequalities in two variables?
To graph the solution set of an inequality with two variables, first graph the boundary with a dashed or solid line depending on the inequality. If given a strict inequality, use a dashed line for the boundary. If given an inclusive inequality, use a solid line. Next, choose a test point not on the boundary.
What is the solution to a polynomial inequality?
To solve a polynomial inequality, first rewrite the polynomial in its factored form to find its zeros. For each zero, input the value of the zero in place of x in the polynomial. Determine the sign (positive or negative) of the polynomial as it passes the zero in the rightward direction.
What is the difference between polynomial and rational inequalities?
When a polynomial inequality is in standard form, with zero on one side, the roots of the polynomial are the critical numbers. When a rational inequality is written as a single algebraic fraction, with zero on one side, the roots as well as the restrictions are the critical numbers.