The Nature of Graphs - Ch 03

1. The Nature of Graphs - Ch 03 Point Symmetry Two distinct points P and P’ are symmetric with respect to a point, M, if and only if _______________________________. Point M is symmetric with respect to ____. M is the midpoint of line segment PP’ itself 3-1 p. 106

2. The Nature of Graphs - Ch 03 Symmetry with Respect to the Origin The graph of a relation S is symmetric with respect to the origin if and only if _______________________whenever (a,b) is an element of S. A function f(x) has a graph that is symmetric with respect to the origin if and only if _____________. (-a,-b) is an element of S f(-x) = -f(x) 3-1 p. 107

3. The Nature of Graphs - Ch 03 Line Symmetry Two distinct points P and P’ are symmetric with respect to a line L if and only if L is the ___________________of the line segment PP’. A point P is symmetric to itself with respect to line L if and only if ______________. perpendicular bisector P is on line L 3-1 p. 108

4. The Nature of Graphs - Ch 03 Definition of Inverse Relations Two relations are inverse relations if and only if one relation contains the element ______ whenever the other relation contains the element (a, b). The inverse of f(x) is written ________. (b, a) f -1(x) 3-3 p. 126

5. The Nature of Graphs - Ch 03 Vertical Asymptote The line x = a is a vertical asymptote for the function f(x) if f(x) approaches ______ or f(x) approaches ________________ as x approaches a from either the left or the right. infinity negative infinity 3-4 p. 135

6. The Nature of Graphs - Ch 03 Horizontal Asymptote The line y = b is a horizontal asymptote for the function f(x) if f(x) approaches b as _______________________ or as _________________________. x approaches infinity x approaches negative infinity 3-4 p. 135

7. The Nature of Graphs - Ch 03 Slant Asymptote The oblique line L is a slant asymptote for a function f(x) if the graph off(x) approaches L as ___________________ or as ___________________________. An oblique line is a line that is _________________________. x approaches infinity x approaches negative infinity neither vertical nor horizontal 3-4 p. 135

8. The Nature of Graphs - Ch 03 Rules for Derivatives Constant Rule: The derivative of a constant function is _________. If f(x) = c, then f ‘ (x) = 0. constant 3-6 p. 151

9. The Nature of Graphs - Ch 03 Rules for Derivatives, continued Power Rule: If f(x) = xn, where n is a rational number, then the derivative of f(x) is… . f ‘ (x) = n x(n-1) 3-6 p. 151

10. The Nature of Graphs - Ch 03 Rules for Derivatives, continued Constant Multiple of a Power Rule: If f(x) = c xn, where c and n are both rational numbers, then the derivative of f(x) is… f ‘ (x) = n c x(n-1) 3-6 p. 151

11. The Nature of Graphs - Ch 03 Rules for Derivatives, continued Sum Rule: If f(x) = g(x) + h(x), then the derivative of f(x) is … f‘ (x) = g‘ (x) + h‘ (x) 3-6 p. 151

12. The Nature of Graphs - Ch 03 Conditions for Continuity A function f(x) is continuous at a point x = c if it satisfies three conditions: (1) the function is defined at c; (2) the function approaches the same y-value to the left and the right of x=c; (3) the y-value that the function approaches from each side is f(c). 3-8 p. 164

13. The Nature of Graphs - Ch 03 Continuity on an Interval A function f(x) is continuous on an interval if it is continuous for each value of x in that interval. 3-8 p. 165

14. The Nature of Graphs - Ch 03 Increasing and Decreasing Functions A function f(x) is increasing if and only if f(x1) < f(x2) whenever x1 < x2. A function f(x) is decreasing if and only if f(x1) > f(x2) whenever x1 < x2. 3-8 p. 168