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HLRGAATPreISM_35799X_04_ch4

# HLRGAATPreISM_35799X_04_ch4 - Chapter 4 Rational Power and...

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Chapter 4: Rational, Power, and Root Functions 4.1: Rational Functions and Gr aphs 1. The only value for x that cannot be used as input is 0. The domain is . It is not possible for this function to output the value 0. The range is . 2. The only value for x that cannot be used as input is 0. The domain is . The function will output only positive values. The range is . 3. The function decreases everywhere it is defined, . It never increases and is never constant. 4. The function increases on . It decreases on . The function is never constant. 5. Because the function is undefined when , the vertical asymptote has the equation . As increases with out bound, the graph of the function will move closer and closer to the graph of . 6. Because the function is undefined when , the vertical asymptote has the equation . As increases with out bound, the graph of the function will move closer and closer to the graph of . 7. Because , the function is even. The graph has symmetry with respect to the y -axis. 8. Because , the function is odd. The graph has symmetry with respect to the origin. 9. Graphs A, B, and C have domain because each has a vertical asymptote at . 10. Graph B has range because it exists above and below the horizontal asymptote at . 11. Graph A has range because it exists above and below the horizontal asymptote at . 12. Graphs C and D have range because each exists only above the horizontal asymptote at . 13. The only graph that would intersect the line exactly one time is graph A. 14. Because graph A exists above and below the horizontal asymptote , its range is . 15. Graphs A, C, and D have the x -axis as a horizontal asymptote. 16. Noting that graph D has a hole, graph C is the only graph that is symmetric with respect to a vertical line. 17. Window C gives the most accurate depiction of the graph. See Figures 17a, 17b and 17c. Figure 17a Figure 17b Figure 17c 18. Window A gives the most accurate depiction of the graph. See Figures 18a, 18b and 18c. Figure 18a Figure 18b Figure 18c Yscl 1 Xscl 1 Yscl 1 Xscl 1 Yscl 1 Xscl 1 3 4.7, 4.7 4 by 3 3.1, 3.1 4 3 4.7, 4.7 4 by 3 6.2, 6.2 4 3 4.7, 4.7 4 by 3 0, 12.4 4 Yscl 1 Xscl 1 Yscl 1 Xscl 1 Yscl 1 Xscl 1 3 9.4, 9.4 4 by 3 3.1, 3.1 4 3 14.4, 4.4 4 by 3 0, 5 4 3 4.7, 4.7 4 by 3 3.1, 3.1 4 1 q , 0 2 h 1 0, q 2 y 0 y 3 y 0 1 0, q 2 y 0 1 q , 0 2 h 1 0, q 2 y 3 1 q , 3 2 h 1 3, q 2 x 3 1 q , 3 2 h 1 3, q 2 ƒ 1 x 2 ƒ 1 x 2 ƒ 1 x 2 ƒ 1 x 2 y 4 0 x 0 x 2 x 2 y 2 0 x 0 x 3 x 3 1 0, q 2 1 q , 0 2 1 q , 0 2 h 1 0, q 2 1 0, q 2 1 q , 0 2 h 1 0, q 2 1 q , 0 2 h 1 0, q 2 1 q , 0 2 h 1 0, q 2

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19. Let , then . To obtain the graph of f , stretch the graph of vertically by a factor of 2. See Figures 19a and 19b. The domain is . The range is . Figure 19a Figure 19b 20. Let , then . To obtain the graph of f , stretch the graph of vertically by a factor of 3 and reflect it across the x -axis or the y -axis. See Figures 20a and 20b. The domain is . The range is . Figure 20a Figure 20b 21. Let , then .
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