Decimal number lines

Learning Objectives Identify decimal critical points (zeros and vertical asymptotes) of a rational expression. Accurately plot decimal values on a number line to create test intervals. Select appropriate test values within each interval. Perform sign analysis on a rational expression for each test interval. Interpret the results from a decimal number line sign chart to solve rational inequalities. Express the solution to a rational inequality using interval notation. How can we quickly determine when a complex fraction like (x - 1.5) / (x + 4.2) is positive or negative without graphing it? 🤔 This tutorial will teach you how to use decimal number lines as a powerful visual tool for analyzing rational expressions. You will learn to find where these expressions are positive,...

TermDefinitionExample Rational ExpressionAn expression that can be written as a fraction P(x)/Q(x), where P(x) and Q(x) are polynomials and Q(x) is not zero.f(x) = (x - 2.5) / (x + 1.8) Critical PointA value of x that makes the numerator or the denominator of a rational expression equal to zero. These points are where the expression can change its sign.For f(x) = (x - 2.5) / (x + 1.8), the critical points are x = 2.5 and x = -1.8. Zero of an ExpressionA value of x that makes the numerator of the rational expression equal to zero, thus making the entire expression equal to zero.For f(x) = (x - 2.5) / (x + 1.8), the zero is at x = 2.5. Vertical AsymptoteA vertical line x = a that the graph of a function approaches but never touches. It occurs at x-values that make the denominator of a ratio...

Finding Critical Points For f(x) = P(x) / Q(x), set P(x) = 0 and Q(x) = 0. Solve these two equations to find all the x-values that will be plotted on the number line. These points divide the number line into test intervals. Sign of a Quotient \frac{(+)}{(+)} = (+), \quad \frac{(-)}{(-)} = (+), \quad \frac{(+)}{(-)} = (-), \quad \frac{(-)}{(+)} = (-) When testing a value from an interval, determine the sign of the numerator and the denominator separately. Use these rules to find the overall sign of the rational expression in that interval.