Of the three functions, all three pass the vertical line test. That is, if you draw a vertical line anywhere on the graph that the function is, that line will only pass through the function once. All three are also invertible functions, which means that there is a function that is capable of "undoing" the original function. And because the functions all pass the vertical line test, they are all able to be differentiated.
a quadratic equation must be in this form ax^2+bx+c=0 (can either be + or -) an exponential just means that the function grows at an exponential rate f(x)=x^2 or x^3
an equation has an equals sign.
There are an infinite number of different quadratic equations. The quadratic formula is a single formula that can be used to find the pair of solutions to every quadratic equation.
Exponential growth is when the amount of something is increasing, and exponential decay is when the amount of something is decreasing.
Beyond the fact that they are both measures derived from probability density functions, I cannot think of any similarity.
Exponential and logarithmic functions are inverses of each other.
a quadratic equation must be in this form ax^2+bx+c=0 (can either be + or -) an exponential just means that the function grows at an exponential rate f(x)=x^2 or x^3
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.
neither linear nor exponential functions have stationary points, meaning their gradients are either always +ve or -ve
Both are polynomials. They are continuous and are differentiable.
Nonlinear relations are mathematical relationships between variables where the graph of the relationship is not a straight line. This means that as one variable changes, the other variable does not change by a constant rate, resulting in a curved or non-linear shape on a graph. Examples of nonlinear relations include quadratic functions, exponential functions, and trigonometric functions.
They are both polynomial functions. A quadratic is of order 2 while a cubic is of order 3. A cubic MUST have a real root, a quadratic need not.
A power function has the equation f(x)=x^a while an exponential function has the equation f(x)=a^x. In a power function, x is brought to the power of the variable. In an exponential function, the variable is brought to the power x.
All linear equations of the form y = mx + b, where m and b are real-valued constants, are functions. A linear equation of the form x = a, where a is a constant is not a function. Functions must be one-to-one. That means each x-value is paired with exactly one y-value.
A linear equation, when plotted, must be a straight line. Such a restriction does not apply to a line graph.y = ax2 + bx +c, where a is non-zero gives a line graph in the shape of a parabola. It is a quadratic graph, not linear. Similarly, there are line graphs for other polynomials, power or exponential functions, logarithmic or trigonometric functions, or any combination of them.
Linear equations are a tiny subset of functions. Linear equations are simple, continuous functions.
The similarities are that they are polynomial functions and therefore continuous and differentiable.A real cubic will has an odd number of roots (and so must have a solution), a quartic has an even number of roots and so may have no solutions.