Rational Exponents and Radical Functions
Algebra II Chp 6 Part 1 Test
F&L Name:__________________________
March 31, 2021
Evaluate the expression without using a calculator. Show your work.
1. 321/5
2. 16
−3
2
3
3. ( √−27)2
5
4. Evaluate √−748 using a calculator. Round the result to two decimal places if appropriate.
5. In physics, transitional kinetic energy E, (in Joules) is given by the equation
𝐸=
1
2
𝑚𝑣 2 , where m represents the mass (in kilograms), and v the velocity (in meters per
second). Find the velocity of a throw baseball at time of release whose mass is 0.148 kg, and
whose transitional kinetic energy is equal to 90.65 Joules.
Simplify the expression. Assume all variable are positive.
−1
6.
27 3
−4
27 3
7. √80 − √245
3
8. √−125𝑥 3
9.
4𝑦 2.7
𝑦 1.35
Let 𝑓(𝑥) = 𝑥 2 − 4, and 𝑔(𝑥) = −𝑥 3 . Perform the indicated operation and state the domain.
10. 𝑓(𝑥) − 𝑔(𝑥)
Domain:_____________________
11. 𝑔(𝑥) ∙ 𝑔(𝑥)
Domain:_____________________
12. 𝑔(𝑓(𝑥))
Domain:______________________
A rental car costs $35 for a one-day rental, plus $0.05 per mile. The total cost (in dollars) is
given by the equation 𝐶(𝑚) = 35 + 0.05𝑚, where m represents the milage. The car averages 32
miles per gallon, and so the total mileage is given by the equation 𝑚(𝑔) = 32𝑔.
13. Find
𝐶(𝑚(𝑔)), and the total cost after using 8 gallons of gas.