Jump to a specific example Instructors Kathryn Boddie View bio Marisa Bjorland View bio Steps for Finding Intercepts, Asymptotes, Domain, and Range From the Graph of a Rational Function Step 1:Find all intercepts. The {eq}x {/eq}-intercept(s) are points {eq}...
A rational equation contains a fraction with a polynomial in both the numerator and denominator — for example; the equation y = (x – 2) / (x^2 – x – 2). When graphing rational equations, two important features are the asymptotes and the holes of the graph. Use algebraic techniques ...
Rational equations can have what are called discontinuities. Nonremovable discontinuities are vertical asymptotes, invisible lines that the graph approaches but does not touch. Other discontinuities are called holes. Finding and graphing a hole often involves simplifying the equation. This leaves a literal...
Rational equations can have what are called discontinuities. Nonremovable discontinuities are vertical asymptotes, invisible lines that the graph approaches but does not touch. Other discontinuities are called holes. Finding and graphing a hole often involves simplifying the equation. This leaves a literal...
Learn how to find vertical asymptotes given a rational function and identify them on a graph. Study vertical asymptote rules and identify horizontal asymptotes. Related to this Question How do you find vertical asymptotes of y = csc(pi x)?
Some functions are continuous from negative infinity to positive infinity, but others break off at a point of discontinuity or turn off and never make it past a certain point. Vertical and horizontal asymptotes are straight lines that define the value th
Knowing how to find the vertex of a parabola enables us to write the equation of a parabola given only limited information about it. What is the vertex of a quadratic function? The vertex of a quadratic function is the vertex of the graph of that function. Given a quadratic function in ...
It is common and perfectly okay to cross a horizontal asymptote. (It's the vertical asymptotes that I'm not allowed to touch.) As I can see in the table of values and from the graph, the horizontal asymptote is thex-axis. horizontal asymptote:y= 0(thex-axis) ...
How do you find the slope of asymptotes of a hyperbola? What is the equation of a line that is parallel to y = -4x + 2 and goes through the point (-4, 9)? Find the equation of the tangent line to the graph of y = (2x + 3)/(3x - 2) at the point (1,5) using the qu...
The slant (or oblique) asymptote for that rational function is a straight (but not horizontal or vertical) line that shows where the graph goes, off to the sides.How do you find the slant (or oblique) asymptote?To find the slant asymptote, do the long division of the numerator by the ...