University:
Felician University
Course:
MATH-002 | Basic Math Skills-Algebra
Academic year:

2020
Views:

63

Pages:

3
Author:

larbiwxcvbn

Behavior of Functions Clues in the crossword puzzle refer to Figures A and B. Figure A piecewise function graph Figure B sinusoidal function graph Across Fig. B: f(0) Fig. A: f(-3) Fig. A: behavior on [1, 3] Fig. A: behavior at x = 3 Fig. A: f(3) Fig. B: the number of intervals for which the graph is constant Down Fig. B: the transformation that makes the graph on [-1, 0] the image of the graph on [0, 1] Fig. B: the characteristic described by y = 4 Fig. A: how the function may be defined Fig. A: behavior on (-3, -1] Fig. B: number of relative maximum values Fig. A: behavior on [-1, 1] **Name** **Symmetry** **Algebraic Tests for Symmetry** **Remember** If an equivalent equation results when: * x is replaced by -x: Then the graph is symmetric to the y-axis * y is replaced by -y: Then the graph is symmetric to the x-axis * x is replaced by -x and y is replaced by -y: Then the graph is symmetric to the origin **Example** Test the relation xy = 16 for symmetry in its graph. Replace x with -x: xy = 16 (-x)y = 16 -xy = 16 Not equivalent to the original equation; graph is not symmetric with respect to the y-axis. Replace y with -y: xy = 16 x(-y) = 16 -xy = 16 Not equivalent to the original equation; graph is not symmetric with respect to the x-axis. Replace x with -x and y with -y: xy = 16 (-x)(-y) = 16 xy = 16 Equivalent to the original equation; graph is symmetric with respect to the origin. **For each relation, write the letter of the type of symmetry in its graph.** (a) only the x-axis (b) only the y-axis (c) the origin (d) both axes and the origin (e) no symmetry 1. x² + y² = 5 2. y = |x| - 5 3. y = x² 4. 5y = 2x + 3 5. x = |y| 6. y = -x³ + 3 7. y² = 2x² + 1 8. |x| + |y| = 4 9. y = -x⁵ Connect your answers in order of the problem numbers. You should be connecting each dot to every other dot without drawing the same line segment twice. **Name** **Period** **Score** **IE** Find the x- and y-intercepts algebraically. Write your solutions as coordinates. 1. y = 3x - 2 x-int: 0 = 3x - 2 x = 2/3 y-int: y = 3(0) - 2 y = -2 (2/3, 0) (0, -2) 2. 2x + y = -8 x-int: 2x + 0 = -8 2x = -8 x = -4 y-int: 2(0) + y = -8 y = -8 (-4, 0) (0, -8) 3. y = x² - 9 x-int: 0 = x² - 9 (x + 3)(x - 3) = 0 x = -3, x = 3 y-int: y = 0² - 9 y = -9 (3, 0), (-3, 0) (0, -9) 4. 2x² + y² = 20 x-int: 2x² + 0² = 20 2x² = 20 x² = 10 x = ±√10 y-int: 2(0)² + y² = 20 y² = 20 y = ±√20 = ±2√5 (√10, 0), (-√10, 0) (0, 2√5), (0, -2√5) 5. y = x² + x + 6 x-int: 0 = x² + x + 6 0 = (x + 3)(x + 2) x = -3, x = -2 y-int: y = 0² + 0 + 6 y = 6 (-3, 0), (-2, 0) (0, 6) 6. y = x³ - x x-int: 0 = x³ - x 0 = x(x² - 1) 0 = x(x + 1)(x - 1) x = 0, x = -1, x = 1 y-int: y = 0³ - 0 y = 0 (0, 0), (-1, 0), (1, 0) (0, 0)