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For the graph of the linear function f(x) = mx + b, m is the _____ and b is the ______.
If the slope m of the graph of a linear function is _______ the function is increasing over its domain.
T or F the slope of a nonvertical line is the average rate of change of the linear function.
When a quadratic equation has a repeated solution, it is called a blank root or a root of blank
The quantity b squared minus 4 a c is called the blank of a quadratic equation. If it is blank, the equation has no real solution
Quadratic equations are sometimes call blank-degree equations.
also known as direction fields. Shows the slope of the solution to the differential equation at any given point.
a mathematical equation that relates a function w/ its derivatives. Can be written in the form g(y)dy=f(x)dx.
False, it is the limit of that
False. y = abs(x − 2) is continuous at x = 2,but is not differentiable at x = 2. (Sharp turn in the graph)
False. If the derivative from the left of a point does not equal the derivative from the right of a point, then the derivative does not exist at that point.
An equation that contains the derivative of a function.
Suppose you are first learning about algebra and you want to find the solution x to the equation y = mx + b. In differential equations, the y is a function and the x is considered to be a common parameter that is common among an expression of many functions. The solution is the function y(x), and the equation is one containing the differential operator composed with the function y, yielding many functions with respect to the same parameter x instead of a scalar m multiplied by a parameter x. In addition to combining like terms, you may combine linearly dependent terms in the solution to a differential equation.
One whose derivatives contain dependent variables with respect to a single independent variable.