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, asympto...
Slant asymptotes can be touched and/or crossed.Find the slant asymptote of the following function: To find the slant asymptote, I need to do the long division: I need to remember that the slant asymptote is the polynomial part of the answer (that is, the asymptote is the part across the...
In trigonometry, the period of a function refers to the distance of a function's wave. Learn how to find the period of a trig function by exploring...
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 function approaches zero, it has...
Let's look at an example of finding horizontal asymptotes: Find the horizontal asymptote of the following function: y=x+2x2+1\small{ \boldsymbol{\color{green}{y = \dfrac{x + 2}{x^2 + 1} }}}y=x2+1x+2 First, notice that the denominator is a sum of squares, so it doesn...
Find the vertical asymptotes. f(x) = 2x - 6 / x + 7 How do you find the vertical asymptotes of a polynomial? Explain how to locate vertical asymptotes. Find all vertical asymptotes of the function Find the vertical asymptotes of the function y = \frac{8x^2 + 1}{9x - 8x^2} Find...
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...
How do you find the horizontal asymptotes of e^x - 2?Question:How do you find the horizontal asymptotes of e^x - 2?Exponential Functions:A basic exponential function has the following form: {eq}f(x)= b^{x} {/eq} where b is a positive constant. The domain of an exponential function...
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