# Graphs

• I. N. Bronshtein
• K. A. Semendyayev

## Abstract

Linear function: y = ax + b (Fig. 2a). The graph—a straight line. The function increases monotonically for a > 0 and decreases monotonically for a < 0; it is constant for a = 0. Intersections with the axes: $$A\left ( -\frac{a}{b},0 \right )$$, B(0, b). For details see p. 239. For b = 0, it represents a direct proportionality: y = ax; the graph is a straight line passing through the origin (Fig. 2b).

## Keywords

Parametric Form Tangent Line Double Point Sine Curve Irrational Function
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Notes

1. (1).
For the solution of the cubic equation see pp. 161–163.Google Scholar
2. (1).
For degree of a curve see p. 239.Google Scholar
3. (2).
For solution of the algebraic equation of the n-th degree see pp. 164–167 and pp. 169–171.Google Scholar
4. (1).
For the definitions and formulas see pp. 223–225.Google Scholar
5. (1).
For theoretical discussion of hyperbolic functions see pp. 229–230; for the tables see pp. 61–65.Google Scholar
6. (1).
For theoretical discussion see pp. 232–233.Google Scholar
7. (1).
In the following M will denote an arbitrary point of the curve with the coordinates x, y.Google Scholar
8. (1).
In general, the conchoid of a curve is the curve obtained from the given one by increasing or decreasing the radius vector of the curve by a constant segment l. If the equation of the given curve in the polar coordinates is ϱ = f(φ), then the equation of its conchoid is ϱ = f(φ) ± l. The conchoid of Nicomedes is the conchoid of the straight line.Google Scholar
9. (1).
For solution of such equations see pp. 161–162.Google Scholar
10. (2).
See footnote on p. 119.Google Scholar
11. (1).
For solution of such equations see pp. 168–169.Google Scholar
12. (1).
The constant denoted on p. 120 by a is here denoted by 2λa and l denoted the diameter 2a. The coordinate system has been changed.Google Scholar
13. (1).
For the involute see p. 294.Google Scholar
14. (2).
For solution of such equations see pp. 168–169.Google Scholar
15. (1).
In other words: If one end point of a non-expansible thread of a given length a is fastened to a material point M and the other end point P is dragged along a straight line (Ox), then the point M draws the tractrix (whence comes the name of the curve; tractus, in Latin, means dragged).Google Scholar