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How do you find the point of tangency?
A tangent is an object, like a line, which touches a curve. The tangent only touches the curve at one point. That point is called the point of tangency. The tangent does not intersect (pass through) the curve.
What is the change in y over change in x?
The gradient (slope) of the curve at the midpoint at which the changes are calculated or the derivative of the curve at that point. These are only crude approximations unless the function is linear or if the changes are taken over very very small intervals. Equivalently, it is the slope of the tangent to the curve.
What would you use to determine whether or not a graph is a function?
I think what you are asking is: "If I have a curve on a plane, how do I know if it is a function or not?". For regular Cartesian coordinates, where x is the independent variable and y is the dependent variable, you can use something called the "vertical line test". If you hold up a line parallel to the y-axis it will intersect the curve. Now if you can move it side to side and it never intersects the curve *more than once* then you have a function (of x). The reason is this: a function is a rule that associates every point in the domain to a single point in the range (also called the codomain). This means that if you are given any point in the domain and evaluate the function at that point you will get one value in the range (this does not need to be a unique value. You can have two different points in the domain taking on the same value in the range; think absolute value or sine curves). So, if we are using the vertical line test and it intersects the curve twice for a single value of x, we know that the curve cannot be a function, since there are two values in the range associated with one value in the domain. On the other hand, if the curve passes the vertical line test i.e. it only intersects the curve once at every point in the domain, then you have a function of x. You can use an analogous "horizontal line test" to see if something is a function of y.
Is tangent in geometry and tangent in trigonometry same?
Yes a tangent is a straight line thattouches a curve at only one point But there is a tangent ratio used in trigonometry
The only unit that cant be used to express volume is?
There are many units that cannot be used to express a volume.There is something missing from your question to request the only unit.
