I need to remember that the slant asymptote is the polynomial part of the answer (that is, the asymptote is the part across the top of the division, set equal to y), not the remainder (that is, not the last value at the bottom). Then my answer is: slant asymptote: y = x + 5...
The end behavior of the rational function is the horizontal asymptote {eq}y = 2 {/eq}. Step 3: If the degree of the numerator is greater than the degree of the denominator, then there is a slant/oblique asymptote (if the degree of the numerator is exactly one larger than the deg...
Determine the degree of the polynomials in the numerator and denominator. The degree of a polynomial is equal to its highest exponential value. In the example equation, the degree of the numerator (x – 2) is 1 and the degree of the denominator (x^2 – x – 2) is 2. Step 4 Determi...
Determine the horizontal asymptote for the graph of the function f(x) = \sqrt{x^2 + x} - x. Find the vertical asymptote, horizontal asymptote and the slant asymptote of the following function. f(x) = (2x^3 - 5x^2 - 19x + 1)/(x^2 - 9) ...
Determine whether or not there are any holes. Find the asymptotes vertical, horizontal, and slant and draw dotted lines to break the graph along those lines and ensure that the graph does not touch them. Create a table of values by taking some random x values (on both sides of the x-in...
In the example above, you would need to graph x + 2 to see that the line moves alongside the graph of your polynomial but never touches it, as shown below. So x + 2 is indeed a slant asymptote of your polynomial. Community Q&A Question Where did the two polynomials come from? Tech...