8 Mid-Chapter Quiz

Do you know HOW?

If z = 30 when x = 3 and y = 2, write the function that models the relationship.

1. z varies jointly with x and y.
2. z varies directly with x and inversely with y.
3. z varies inversely with the product of x and y.

Is the relationship between the values in the table a direct variation, an inverse variation, or neither?

4. x	y
   22	104
   35	174
   48	239
   54	269

5. x	y
   2	− 4.8 negative 4.8
   6	− 14.4 negative , 14.4
   12	− 28.8 negative , 28.8
   19	− 45.6 negative , 45.6

6. x	y
   15	2.4
   18	2
   20	1.8
   45	0.8

Suppose that x and y vary inversely. Write a function that models the inverse variation.

7. x = 13 x equals 13  when y = 17 y equals 17
8. x = − 12 x equals negative 12  when y = 4 y equals 4
9. x = − 52 x equals negative 52  when y = 1 4 y equals , 1 fourth

Explain how the graph of y 2 y sub 2  is related to the graph of y 1 . y sub 1 , .

10. y 1 = 4 x  and  y 2 = 9 x y sub 1 , equals , 4 over x , and , y sub 2 , equals , 9 over x
11. y 1 = 1 x  and  y 2 = 1 x + 5 y sub 1 , equals , 1 over x , and , y sub 2 , equals , 1 over x , plus 5
12. y 1 = 1 x − 1 + 2  and  y 2 = 1 x + 1 − 2 y sub 1 , equals . fraction 1 , over x minus 1 end fraction . plus 2 , and , y sub 2 , equals . fraction 1 , over x plus 1 end fraction . minus 2

Find any holes and vertical or horizontal asymptotes for the graph of each rational function.

13. y = 1 x 2 + 3 x − 10 y equals . fraction 1 , over x squared , plus 3 x minus 10 end fraction
14. y = x + 2 ( x + 2 ) ( x − 3 ) y equals . fraction x plus 2 , over open , x plus 2 , close . open , x minus 3 , close end fraction
15. y = x − 1 x 2 − 2 x + 1 y equals . fraction x minus 1 , over x squared , minus 2 x plus 1 end fraction
16. y = 5 x − 2 x + 2 y equals . fraction 5 x minus 2 , over x plus 2 end fraction

Sketch the graph of each rational function. Then identify the domain and range.

17. y = − 2 x y equals , negative 2 over x
18. y = 5 x + 3 − 4 y equals . fraction 5 , over x plus 3 end fraction . minus 4
19. y = x 2 − 9 2 x + 6 y equals . fraction x squared , minus 9 , over 2 x plus 6 end fraction
20. y = 3 x x 3 − x y equals . fraction 3 x , over x cubed , minus x end fraction
21. y = x + 3 x − 3 y equals . fraction x plus 3 , over x minus 3 end fraction
22. y = x 2 − 2 x x − 2 y equals . fraction x squared , minus 2 x , over x minus 2 end fraction

Do you UNDERSTAND?

Open-Ended Write a rational function with the given characteristics.

23. a vertical asymptote at x = 8 x equals 8  and a horizontal asymptote at y = 0 y equals 0
24. a vertical asymptote at x = − 4 x equals negative 4  and a horizontal asymptote at y = 3 y equals 3
25. a hole at x = − 5 x equals negative 5  and a vertical asymptote at x = 2 x equals 2
26. Reasoning How many inverse variation functions have (2, 3) as a solution?
27. Reasoning The graph of an inverse variation function contains the point (a, b). Using a and b, identify 3 other points on the graph.
28. Reasoning Graph the equations y = x 2 + x − 6 x 2 − 5 x + 6 y equals . fraction x squared , plus x minus 6 , over x squared , minus 5 x plus 6 end fraction  and y = x + 3 x − 3 . y equals . fraction x plus 3 , over x minus 3 end fraction . .  Are they equivalent? Explain.

Table of Contents