Yes, to the left (towards minus infinity).
Yes, to the left (towards minus infinity).
Yes, to the left (towards minus infinity).
Yes, to the left (towards minus infinity).
Yes, to the left (towards minus infinity).
tangent, cosecants, secant, cotangent.
Asymptotes are one way - not the only way, but one of several - to analyze the general behavior of a function.
neither linear nor exponential functions have stationary points, meaning their gradients are either always +ve or -ve
Exponential and logarithmic functions are different in so far as each is interchangeable with the other depending on how the numbers in a problem are expressed. It is simple to translate exponential equations into logarithmic functions with the aid of certain principles.
Yes.
Three types of asymptotes are oblique/slant, horizontal, and vertical
If a hyperbola is vertical, the asymptotes have a slope of m = +- a/b. If a hyperbola is horizontal, the asymptotes have a slope of m = +- b/a.
Many functions actually don't have these asymptotes. For example, every polynomial function of degree at least 1 has no horizontal asymptotes. Instead of leveling off, the y-values simply increase or decrease without bound as x heads further to the left or to the right.
No, it will always have one.
asymptote
tangent, cosecants, secant, cotangent.
x-axis
Asymptotes are one way - not the only way, but one of several - to analyze the general behavior of a function.
finding vertical asymptotes is easy. lets use the equation y = (2x-2)/((x^2)-2x-3) since its a rational equation, all we have to do to find the vertical asymptotes is find the values at which the denominator would be equal to 0. since this makes it an undefined equation, that is where the asymptotes are. for this equation, -1 and 3 are the answers for the vertical ayspmtotes. the horizontal asymptotes are a lot more tricky. to solve them, simplify the equation if it is in factored form, then divide all terms both in the numerator and denominator with the term with the highest degree. so the horizontal asymptote of this equation is 0.
x axis
Exponential and logarithmic functions are inverses of each other.
There are no points of discontinuity for exponential functions since the domain of the general exponential function consists of all real values!