Section 7 3 Graphing Reciprocal Functions ALGEBRA 2

Section 7: 3 Graphing Reciprocal Functions ALGEBRA 2 ROGER CARESIA

Limitations on Domain Determine the values of x for which is not defined. Find the value for which the denominator equals 0. Solve for x. Simplify Answer: x = − 8.

Determine Properties of Reciprocal Functions A. Identify the asymptotes, domain, and range of the function. Identify the x-values for which f(x) is undefined. x– 2 = 0 x= 2 f(x) is not defined when x = 2. So, there is an asymptote at x = 2.

Determine Properties of Reciprocal Functions From x = 2, as x-values decrease, f(x)-values approach 0, and as x-values increase, f(x)-values approach 0. So, there is an asymptote at f(x) = 0. Answer: asymptotes: x = 2, y = 0; D = {x|x ≠ 2} or (−∞, 2) ∪ (2, +∞); R = {y|y ≠ 0} or (−∞, 0) ∪ (0, +∞)

Determine Properties of Reciprocal Functions B. Identify the asymptotes, domain, and range of the function. Identify the x-values for which f(x) is undefined. x+2 = 0 x = – 2 f(x) is not defined when x = – 2. So, there is an asymptote at x = – 2.

Determine Properties of Reciprocal Functions From x = – 2, as x-values decrease, f(x)-values approach 1, and as x-values increase, f(x)-values approach 1. So, there is an asymptote at f(x) = 1. Answer: asymptotes: x = − 2, y = 1; D = {x|x ≠ 2} or (−∞, − 2) ∪ (− 2, +∞); R = {y|y ≠ 1} or (−∞, 1) ∪ (1, +∞)

A. Identify the asymptotes of the function. A. x = 3 and f(x) = 3 B. x = 0 and f(x) = – 3 C. x = – 3 and f(x) = – 3 D. x = – 3 and f(x) = 0

B. Identify the domain and range of the function. A. D = {x | x ≠ – 3}; R = {f(x) | f(x) ≠ – 4} B. D = {x | x ≠ 3}; R = {f(x) | f(x) ≠ 0} C. D = {x | x ≠ 4}; R = {f(x) | f(x) ≠ – 3} D. D = {x | x ≠ 0}; R = {f(x) | f(x) ≠ 4}

Graph Transformations A. Graph the function State the domain and range. This represents a transformation of the graph of a = – 1: h = – 1: k = 3: The graph is reflected across the x-axis. The graph is translated 1 unit left. There is an asymptote at x = – 1. The graph is translated 3 units up. There is an asymptote at f(x) = 3.

Graph Transformations Answer: Domain: {x│x ≠ – 1} Range: {f(x)│f(x) ≠ 3}

Graph Transformations B. Graph the function State the domain and range. This represents a transformation of the graph of a = – 4: The graph is stretched vertically and reflected across the x-axis. h = 2: The graph is translated 2 units right. There is an asymptote at x = 2.

Graph Transformations k = – 1: The graph is translated 1 unit down. There is an asymptote at f(x) = – 1. Answer: Domain: {x│x ≠ 2} Range: {f(x)│f(x) ≠ – 1}

A. Graph the function A. B. C. D.

B. State the domain and range of A. Domain: {x│x ≠ – 1}; Range: {f(x)│f(x) ≠ – 2} B. Domain: {x│x ≠ 4}; Range: {f(x)│f(x) ≠ 2} C. Domain: {x│x ≠ 1}; Range: {f(x)│f(x) ≠ – 2} D. Domain: {x│x ≠ – 1}; Range: {f(x)│f(x) ≠ 2}

Write Equations A. COMMUTING A commuter train has a nonstop service from one city to another, a distance of about 25 miles. Write an equation to represent the travel time between these two cities as a function of rail speed. Then graph the equation. Solve the formula r t = d for t. rt = d Original equation. Divide each side by r. d = 25

Write Equations Graph the equation Answer:

Write Equations B. COMMUTING A commuter train has a nonstop service from one city to another, a distance of about 25 miles. Explain any limitations to the range and domain in this situation. Answer: The range and domain are limited to all real numbers greater than 0 because negative values do not make sense. There will be further restrictions to the domain because the train has minimum and maximum speeds at which it can travel.

A. TRAVEL A commuter bus has a nonstop service from one city to another, a distance of about 76 miles. Write an equation to represent the travel time between these two cities as a function of rail speed. A. B. C. D.

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