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1.Write an equation that expresses the relationship. Use k for the constant of
proportionality.
r varies directly as the square of s and inversely as the cube of t.
B) r =
2.Solve the problem.
Is there y-axis symmetry for the rational function f(x) =
?
A) No
3. Solve.
The amount of time it takes a swimmer to swim a race is inversely proportional to the average speed
of the swimmer. A swimmer finishes a race in 30 seconds with an average speed of 5 feet per second.
Find the average speed of the swimmer if it takes 25 seconds to finish the race.
C) 6 feet per second
4. Find the indicated intercept(s) of the graph of the function.
y-intercept of f(x) =
B) none
5. Solve.
While traveling at a constant speed in a car, the centrifugal acceleration passengers feel while the car
is turning is inversely proportional to the radius of the turn. If the passengers feel an acceleration of
10 feet per second per second when the radius of the turn is 100 feet, find the acceleration the
passengers feel when the radius of the turn is 200 feet.
A) 5 feet per second per second
6. Find the domain of the rational function.
f(x) =
B) all real numbers
7. Graph the rational function.
f(x) =
B)
8. Is there y-axis symmetry for the rational function f(x) =
?
B) No
9.Solve the rational inequality and graph the solution set on a real number line. Express
the solution set in interval notation.
≤0
D) (-∞, -9) or [-1, ∞)
10. Solve the problem.
The time in hours it takes a satellite to complete an orbit around the earth varies directly as the radius
of the orbit (from the center of the earth) and inversely as the orbital velocity. If a satellite completes
an orbit
above the earth in
satellite to complete an orbit if it is at
as the radius of the earth.)
at a velocity of
how long would it take a
above the earth at a velocity of
(Use
B) 25.79 hours
11. Write an equation that expresses the relationship. Use k as the constant of variation.
a varies jointly as b and the square of h.
A) a = kbh2
12. Solve the problem.
If y varies directly as the cube of x, and y = 4 when x = 2, find y when x = 8.
C) 256
13. If y varies inversely as x, find the inverse variation equation for the situation.
y = 70 when x = 4
D) y =
14. Use the graph of the rational function shown to complete the statement.
As x→-2+, f(x)→ ?
B) -∞
15. Solve the rational inequality and graph the solution set on a real number line. Express
the solution set in interval notation.
≥0
D) (3, 5]
16. Find the horizontal asymptote, if any, of the graph of the rational function.
f(x) =
B) y = 0
17. Solve the rational inequality and graph the solution set on a real number line. Express
the solution set in interval notation.
>0
A) (-∞, -2) or (6, ∞)
18. Write an equation that expresses the relationship. Use k as the constant of variation.
q varies jointly as r and the cube of s.
B) q = krs3
19.Write an equation that expresses the relationship. Use k as the constant of variation.
w varies inversely as the square of y.
A) w =
20. Solve the polynomial inequality and graph the solution set on a number line. Express
the solution set in interval notation.
(x + 4)(x + 3)(x - 5) > 0
C) (-4, -3) (5, ∞)