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Ch 8 Test Review Given: y varies directly as x. Write each variation function. ( direct: y = kx ) 1. Y = 35 when x = 2.5 2. Y = 3 when x = 12 3. The distance, d, that Stephen runs each day varies directly with the amount of time, t, that he runs. If d = 10 miles when t = 1.25 hours. Find d when t = 1.75 h. Given: y varies inversely as x. Write each inverse function. (inverse: y = k/x) 4. y = 4 when x = 2 5. y = 6 when x =
2
3
6. y varies directly with x and inversely with z. Write the combined variation function, given that y = 15 when x = 10 and z = 2. 7. The time, t, it takes for a bus to travel a specific distance varies inversely with its average speed, r. It takes the bus 2.2 hours to travel between two cities at 50 mph. How long will the same drive take at 40 mph? Determine whether the data set represents a direct variation, inverse variation, or neither. Then name the value of k. 8. x y 3 30 45 2 6 15 9. x y 3 30 6 60 8 80 Simplify. Identify any x values for which the expression is undefined. 10. 15x 3
5x 2 +10x
11. x 2 − 2x − 3
x 2 + 5x + 4
Multiply. Assume that all expressions are defined. 12. x + 3 2x + 4
•
x + 2 x2 − 9
x − 4 x 2 + 5x + 6
•
x + 3 x 2 + x − 20
13. Divide. Assume that all expressions are defined. 14. 12 x 3 y 6 6 y 2
÷
9 xy
3x
!!!!"
15. !!
! ! !!"
÷ ! ! !!! Add or subtract. Identify any x values for which the expression is undefined. 16. 3
5x
−
x − x − 2 x +1
2
17. x−5
x+4
−
x + 9x + 20 x + 5
2
Solve each equation. Be sure to look for extraneous solutions! !
!
!
18. !!! − !!! = ! ! !!!!!" !
19. !!! =
!!!!
!!!
Graph & identify all critical information 20. f ( x) =
3x − 6
x+4
x-­‐‑int: ___________ y-­‐‑int: ___________ V.A.: ___________ H.A.: ___________ Domain:_______________ 21. f ( x) =
x 2 − 2 x − 15
x+3
Hole: ___________ 22. f (x) =
3x 2 − 6x
x2 − 9
Simplified function:____________________ x-­‐‑int: ___________ y-­‐‑int: ___________ V.A.: ___________ H.A.: ___________ 23. 𝑓 𝑥 =
!!
!!!
− 3 VA:___________________ HA:__________________ Domain: ______________ Range: _________________ Solve each inequality. Be sure to show your number line. !
!
!
!
24. 2 − < !
!"
!
!
25. 𝑥 + ≤
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