267 2.6 Graphs of Basic Functions Write an equation for each of the following, and sketch the graph. 9. the line through 1-2, 12 and 14, -12 10. the horizontal line through 12, 32 11. the circle with center 12, -12 and radius 3 12. the circle with center 10, 22 and tangent to the x-axis 13. the line through 13, -52 with slope - 5 6 14. the vertical line through 1-4, 32 15. the line through 1-3, 22 and parallel to the line 2x + 3y = 6 16. the line through the origin and perpendicular to the line 3x - 4y = 2 Determine whether or not each equation has a circle as its graph. If it does, give the center and the radius. 17. x2 + y2 - 4x + 2y = 4 18. x2 + y2 + 6x + 10y + 36 = 0 19. x2 + y2 - 12x + 20 = 0 20. x2 + y2 + 2x + 16y = -61 21. x2 + y2 - 2x + 10 = 0 22. x2 + y2 - 8y - 9 = 0 Solve each problem. 23. Find the coordinates of the points of intersection of the line y = 2 and the circle with center at 14, 52 and radius 4. 24. Find the shortest distance from the origin to the graph of the circle with equation x2 + y2 - 10x - 24y + 144 = 0. For each relation, (a) find the domain and range, and (b) if the relation defines y as a function ƒ of x, rewrite the relation using function notation and find ƒ1-22. 25. x - 4y = -6 26. y2 - x = 5 27. 1x + 222 + y2 = 25 28. x2 - 2y = 3 2.6 Graphs of Basic Functions ■ Continuity ■ The Identity, Squaring, and Cubing Functions ■ The Square Root and Cube Root Functions ■ The Absolute Value Function ■ Piecewise-Defined Functions ■ The Relation x =y 2 Continuity The graph of a linear function—a straight line—may be drawn by hand over any interval of its domain without picking the pencil up from the paper. In mathematics we say that a function with this property is continuous over any interval. The formal definition of continuity requires concepts from calculus, but we can give an informal definition at the college algebra level. Continuity (Informal Definition) A function is continuous over an interval of its domain if its hand-drawn graph over that interval can be sketched without lifting the pencil from the paper.
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