Slant (Oblique) AsymptotesVerticalHorizontalSlantExamplesPurplemath In the previous section, covering horizontal asymptotes, we learned how to deal with rational functions where the degree of the numerator was equal to or less than that of the denominator. But what happens if the degree is greater ...
Domain and Range:The domain of a function is the set of all possible inputs {eq}x {/eq} for the function. The range of a function is the set of all possible outputs {eq}y {/eq}. We will use these steps and definitions to find the intercepts, asympt...
Find vertical asymptotes, if any of f(x) = \frac{x^3 - 10x^2 + 16x}{x^2 - 8x} Find the vertical asymptotes of f(x) = tan(x). Find the vertical asymptotes of y = \frac{2x}{\sqrt{x^2 + x - 3} - 3}. Find the vertical asymptotes (if any) of f (x) = {x^2 - ...
Explain how to find which method of depreciation is to be used based on the asset. Explain the cosine and cotangent trigonometric functions. How can I find the slope of a line on a graph with no number given as the x or y? How can one determine how many vertical asymptotes there are ...
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 gra
Find the horizontal asymptote of the following function: First, notice that the denominator is a sum of squares, so it doesn't factor and has no real zeroes. In other words, this rational function has no vertical asymptotes. So we're okay on that front. As mentioned above, the horizontal...
adjacent to an acute angle with a known measure as long as we know the measure of the side opposite that angle. When we graph tangent functions, we see that the y-values have a range of negative infinity to positive infinity, with vertical asymptotes indicating where the graph has no ...
Vertical Asymptotes: First Steps To find a vertical asymptote, first write the function you wish to determine the asymptote of. Most likely, this function will be a rational function, where the variable x is included somewhere in the denominator. As a rule, when the denominator of a rational...
The domain of a trigonometric function refers to the set of input values it is defined and valid for. The secant, cosecant, and cotangent functions have restricted domains due to their asymptotes. What is the trigonometric range? The range of a trigonometric function refers to the set of poss...
Vertical Asymptotes: First Steps To find a vertical asymptote, first write the function you wish to determine the asymptote of. Most likely, this function will be a rational function, where the variable x is included somewhere in the denominator. As a rule, when the denominator of a rational...