A cubic equation adopts the form ax^3 + bx^2 + cx + d, where a =/= 0
If a > 0, the graph will look like this:
If a < 0, the graph will look like this:
ax^3 + bx^2 + cx + d can also be arranged into the form a(x-h)^3 + k, and hence helps you to determine the translations.
If h > 0, the curve moves h units to the left
If h < 0, the curve moves h units to the right
If k > 0, the curve moves k units up
If k < 0, the curve moves k units down
An inverse function, as the name suggests, is the inverse of the original function. The domain of the original function will be the range of the inverse function; the range of the original function will be the domain of the inverse function.
While the function is denoted by f(x), inverse function is denoted by ƒ−1(x). In order to find the inverse of a function, you simply make the independent variable “x” the subject.
For example, the inverse of y = mx + c will be
(y – c)/m = x
Because we always want “x” to be the independent variable, we swap the x and y, the inverse function will therefore be
y = (x – c)/m
ƒ−1(x) = (x – c)/m
Please note that an inverse function is a reflection of the original function in y=x, meaning they are symmetrical about the line y = x.
Suppose you have a parabola, and you want to find the gradient of the parabola at a certain coordinate, you will then draw a straight line that touches that one and only point and calculate its gradient. This line is called the tangent. Tangent, therefore is a line that touches only one single point of the curve.