1.7A.1 MATHPOWER TM 12, WESTERN EDITION Chapter 1 Transformations 1.7A

If f(x) = x, then represents a reciprocal function. 1.7A.2

When f(x)then is less than -1 is -1 is between -1 and 0 is 0 is between 0 and 1 is 1 is greater than 1 1.7A.3 y = x Comparing y = f(x) and The graph ofcan be obtained from the graph of y = f(x), using the following rules: y = 1/x

Where the value of the original function is positive, the value of the reciprocal function is. Where the value of the original function is negative, the value of the reciprocal function is If the value of the original function increases over an interval, the value of the reciprocal function over the same interval. If the value of the original function decreases over an interval, the value of the reciprocal function over the same interval. As the absolute value of the original function increases, the absolute value of the reciprocal function 1.7A.4 Comparing y = f(x) and

Sketching the Graphs of y = f(x) and Draw a vertical asymptote at x = 3. Plot the points that are the same for both. When f(x) < -1, points are transformed to between -1 and 0 (visualize the idea of an inverse of the points). When f(x) is between -1 and 0, points are transformed to less than -1. When f(x) is between 0 and 1, points are transformed to greater than 1. When f(x) > 1, points are transformed to between 0 and A.5 y = f(x)

Since there are no real zeros for f(x), there are for Since f(x) is always positive, is always As | x | increases for f(x), approaches A.6 Sketch the graph of from the graph f(x) = x Sketching the Graph of f(x) = x (0, 3) from y = f(x)

y = f(x) Sketching the Graph of y = There is a vertical asymptote at x = 0. Plot (1, -1) and (-1, 1). As the absolute value of the original function approaches 0, the absolute value of the reciprocal function increases. The points on the graph of f(x), that are greater than y = 1, correspond to the points between the x-axis and y = 1 on the reciprocal function. Points farther from the line of y = 1, correspond to points closer to the x-axis. The points on the graph of f(x) between the x-axis and y = 1 correspond to the points above the line y = 1 on the reciprocal function. Points closer to the x-axis, correspond to points farther away from the line y = A.7 from y = f(x)

where f(x) is a quadratic function. Given the graph of G(x), sketch the graph of f(x) and find its equation. The y-intercept of G(x) is The graph of y = x 2 has been translated units to the right and unit up: Therefore, f(x) =. The point (2, 1) is the same for both functions. 1.7A.8 Finding the Equation and Graph of f(x) from Use the y-intercept of (0, 5):

Suggested Questions: Pages 56 and 57 1, 2, 7, 9-11, 19, A.9

1.7B.1 MATHPOWER TM 12, WESTERN EDITION Chapter 1 Transformations 1.7B

Recall that | x | is equal to x if x ≥ 0, and equal to -x if x ≤ 0. When x ≥ 0, the graph consists of a line defined by y = x. When x ≤ 0, the graph consists of a line defined by y = -x. 1.7B.2 f(x) = |x| The Absolute Value Function

y = 2x Sketch the graph of y = 2x The points on the graph of y = 2x - 3 that are below the x-axis, are reflected in the x-axis. 1.7B.3 Sketch the graph of y = | 2x - 3 |. Sketching the Absolute Value of a Function 2. The points on the graph of y = 2x - 3 that are on or above the x-axis, are invariant points.

y = x B.4 Sketch the graph of y = | x |. Sketching the Absolute Value of a Function 2. Sketch the invariant points. 3. Reflect the points of y = x that are below the x-axis. 1. Sketch the graph of y = x

y = x B.5 Sketching the Absolute Value of a Function

Suggested Questions: Pages 56 and 57 25, 29, 32-36, 39, 42-45, B.6