Considering an asymptote as a tangent to the curve "at infinity", the asymptote is the straight line itself.
A sign chart helps you record data about a function's values around its _____ and _____ asymptotes. zeros vertical
Asymptotes are one way - not the only way, but one of several - to analyze the general behavior of a function.
Assuming the domain is unbounded, the linear function continues to be a linear function to its end.
No a linear equation are not the same as a linear function. The linear function is written as Ax+By=C. The linear equation is f{x}=m+b.
true
When you graph a tangent function, the asymptotes represent x values 90 and 270.
Not sure what non-verticle means, but a rational function can have up to 2 non-vertical asymptotes,
2
To solve for asymptotes of a function, you typically look for vertical, horizontal, and oblique asymptotes. Vertical asymptotes occur where the function approaches infinity, typically at values where the denominator of a rational function is zero but the numerator is not. Horizontal asymptotes are determined by analyzing the behavior of the function as it approaches infinity; for rational functions, this involves comparing the degrees of the polynomial in the numerator and denominator. Oblique asymptotes occur when the degree of the numerator is one higher than that of the denominator, and can be found using polynomial long division.
A sign chart helps you record data about a function's values around its _____ and _____ asymptotes. zeros vertical
Asymptotes
Asymptotes are one way - not the only way, but one of several - to analyze the general behavior of a function.
No, it will always have one.
When you plot a function with asymptotes, you know that the graph cannot cross the asymptotes, because the function cannot be valid at the asymptote. (Since that is the point of having an asymptotes - it is a "disconnect" where the function is not valid - e.g when dividing by zero or something equally strange would occur). So if you graph is crossing an asymptote at any point, something's gone wrong.
sign chart; zeros
Near a function's vertical asymptotes, the function's values can approach positive or negative infinity. This behavior occurs because vertical asymptotes represent values of the independent variable where the function is undefined, causing the outputs to increase or decrease without bound as the input approaches the asymptote. Consequently, as the graph approaches the asymptote, the function's values spike dramatically, either upwards or downwards.
I believe the maximum would be two - one when the independent variable tends toward minus infinity, and one when it tends toward plus infinity. Unbounded functions can have lots of asymptotes; for example the periodic tangent function.