The " current gain " of a bipolar transistor, h < sub > FE </ sub > or h < sub > fe </ sub >, is normally given as a dimensionless number, the ratio of I < sub > c </ sub > to I < sub > b </ sub > ( or slope of the I < sub > c </ sub >- versus-I < sub > b </ sub > graph, for h < sub > fe </ sub >).

We consider now the graph of the function f{t} on Af.

In some neighborhood in the f-plane of any ordinary point of the graph, the function f is a single-valued, continuous function.

The graph of a function | graph of the absolute value function for real numbers

The b value compresses the graph of the function horizontally if greater than 1 and stretches the function horizontally if less than 1, and like a, reflects the function in the y-axis when it is negative.

The graph of a function with a horizontal, vertical, and oblique asymptote.

For curves given by the graph of a function, horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to Vertical asymptotes are vertical lines near which the function grows without bound.

Asymptotes convey information about the behavior of curves in the large, and determining the asymptotes of a function is an important step in sketching its graph.

Horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to +∞ or −∞.

The line x = a is a vertical asymptote of the graph of the function

The graph of this function does intersect the vertical asymptote once, at ( 0, 5 ).

It is impossible for the graph of a function to intersect a vertical asymptote ( or a vertical line in general ) in more than one point.

The graph of a function can have two horizontal asymptotes.

Horizontal asymptotes are horizontal lines that the graph of the function approaches as.

* A Gaussian function, a specific kind of function whose graph is a bell-shaped curve

The graph of f has at least one component whose support is the entire interval Aj.

If the function f is not linear ( i. e. its graph is not a straight line ), however, then the change in y divided by the change in x varies: differentiation is a method to find an exact value for this rate of change at any given value of x.

In classical geometry, the tangent line to the graph of the function f at a real number a was the unique line through the point ( a, f ( a )) that did not meet the graph of f transversally, meaning that the line did not pass straight through the graph.

The derivative of y with respect to x at a is, geometrically, the slope of the tangent line to the graph of f at a.

The slope of the tangent line is very close to the slope of the line through ( a, f ( a )) and a nearby point on the graph, for example.

If f is a continuous function, meaning that its graph is an unbroken curve with no gaps, then Q is a continuous function away from.

If the limit exists, meaning that there is a way of choosing a value for Q ( 0 ) that makes the graph of Q a continuous function, then the function f is differentiable at a, and its derivative at a equals Q ( 0 ).

Differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change while integral calculus is defined informally to be the area of the region in the xy-plane bounded by the graph of f, the x-axis, and the vertical lines and, such that areas above the axis add to the total, and the area below the x axis subtract from the total.

In graph theory, an isomorphism between two graphs G and H is a bijective map f from the vertices of G to the vertices of H that preserves the " edge structure " in the sense that there is an edge from vertex u to vertex v in G if and only if there is an edge from ƒ ( u ) to ƒ ( v ) in H. See graph isomorphism.

is defined informally to be the area of the region in the xy-plane bounded by the graph of f, the x-axis, and the vertical lines and, such that area above the x-axis adds to the total, and that below the x-axis subtracts from the total.

f ( x ) whose graph crosses through the origin, that is, whose y-intercept is 0, has the following properties:

When x and y are real variables, the derivative of f at x is the slope of the tangent line to the graph of f at x.

If x and y are vectors, then the best linear approximation to the graph of f depends on how f changes in several directions at once.

We must now show that on some component of the graph there exist two points for which the corresponding diagonal points in the C-plane are on opposite sides of C.

One of the oldest and most accessible parts of combinatorics is graph theory, which also has numerous natural connections to other areas.

The questions range from counting ( e. g., the number of graphs on n vertices with k edges ) to structural ( e. g., which graphs contain Hamiltonian cycles ) to algebraic questions ( e. g., given a graph G and two numbers x and y, does the Tutte polynomial T < sub > G </ sub >( x, y ) have a combinatorial interpretation ?).

g ( x, y ) is the graph of the function g. A sketch of the graph of such a function or relation would consist of all the salient parts of the function or relation which would include its relative extrema, its concavity and points of inflection, any points of discontinuity and its end behavior.

Logical formulas are discrete structures, as are proofs, which form finite trees or, more generally, directed acyclic graph structures ( with each inference step combining one or more premise branches to give a single conclusion ).

Its distinguishing feature is that the schema, viewed as a graph in which object types are nodes and relationship types are arcs, is not restricted to being a hierarchy or lattice.

The PPF is a table or graph ( as at the right ) showing the different quantity combinations of the two goods producible with a given technology and total factor inputs, which limit feasible total output.

An-extractor is a bipartite graph with nodes on the left and nodes on the right such that each node on the left has neighbors ( on the right ), which has the added property that

** In power engineering, a " bus " is any graph node of the single-line diagram at which voltage, current, power flow, or other quantities are to be evaluated.

This graph is planar ( it is important to note that we are talking about the graphs that have some limitations according to the map they are transformed from only ): it can be drawn in the plane without crossings by placing each vertex at an arbitrarily chosen location within the region to which it corresponds, and by drawing the edges as curves that lead without crossing within each region from the vertex location to each shared boundary point of the region.

More precisely, he showed that a random graph on vertices, formed by choosing independently whether to include each edge with probability has, with probability tending to 1 as goes to infinity, at most cycles of length or less, but has no independent set of size Therefore, removing one vertex from each short cycle leaves a smaller graph with girth greater than in which each color class of a coloring must be small and which therefore requires at least colors in any coloring.

In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects from a certain collection.

Still other methods in phonology ( e. g. Optimality Theory, which uses lattice graphs ) and morphology ( e. g. finite-state morphology, using finite-state transducers ) are common in the analysis of language as a graph.

The introduction of probabilistic methods in graph theory, especially in the study of Erdős and Rényi of the asymptotic probability of graph connectivity, gave rise to yet another branch, known as random graph theory, which has been a fruitful source of graph-theoretic results.

One reason to be interested in such a question is that many graph properties are hereditary for subgraphs, which means that a graph has the property if and only if all subgraphs have it too.

Again, some important graph properties are hereditary with respect to induced subgraphs, which means that a graph has a property if and only if all induced subgraphs also have it.