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1.1 Version 1 Answers
1.1 Version 2 Answers
1.1 Version 3 Answers
1. No
2. A. 3 B. -0.2 C. 0,3 D. -0.8 E. domain [-2,4] range: [-1,3] f. [-2,1]
3. A. f(-4)=-2 g(3)=4 f(-3) = -1 g(2) = 2 B. -2,2 C. -3,4 D. [0,4] E. domain [-4,4] range [-2,3] F. domain [-4,3] range [5,4]
4. Yes, domain [-2,2] range [-1,2]
5. Yes, domain [-3,2] range [-3,-2)U[-1,3]
6. A spherical balloon with radius r inches has a volume V(r) = 4/3 pi r^3. Find an expression that represents the amount of air required to inflate the balloon from a radius of r inches to a radius of r + 5 inches. (Express your answer in terms of pi and r.)
Answer: 4pi/3(15r^2+75r+125)
A spherical balloon with radius r inches has a volume V(r) = 4/3 pi r^3. Find an expression that represents the amount of air required to inflate the balloon from a radius of r inches to a radius of r + 2 inches. (Express your answer in terms of pi and r.)
Answer: 4pi/3(6r^2+12r+8)
7. Evaluate the difference quotient for the given function. Simplify your answer.
f(x) = 4 + 4x –x^2, (f(5+h)-f(5))/h Answer: -h-6
Evaluate the difference quotient for the given function. Simplify your answer.
f(x) = 5 + 3x –x^2, (f(3+h)-f(3))/h Answer: -h-3
Evaluate the difference quotient for the given function. Simplify your answer.
f(x) = 5 + 4x –x^2, (f(3+h)-f(3))/h Answer: -h-2
8. –h^2-3ah-3a^2
9. -1/ax
10. f(x) = (x+4)/(x^2 – 9) Answer: (-infinity,-3)U(-3,3)U(3,infinity)
f(x) = (x+4)/(x^2 – 25) Answer: (-infinity,-5)U(-5,5)U(5,infinity)
11. Find the domain of the function. (Enter your answer using interval notation.)
f(x) = (5x^3-1)/(x^2+2x-3) Answer: (-infinity,-3)U(-3,1)U(1,infinity)
f(x) = (3x^3-4)/(x^2+4x-12) Answer: (-infinity,-6)U(-6,2)U(2,infinity)
f(x) = (4x^3-1)/(x^2+2x-8) Answer: (-infinity,-4)U(-4,2)U(2,infinity)
12. Find the domain of the function. (Enter your answer in interval notation.)
h(x) = 1/(sqrt(x^2-4x)^1/4) Answer: (-infinity,0)U(4,infinity)
h(x) = 1/(sqrt(x^2-6x)^1/4) Answer: (-infinity,0)U(6,infinity)
13. Find the domain of the function. (Enter your answer using interval notation.)
f(x) = {x+6 if x <0
{3 –x if x>= 0
Answer: (-infinity, infinity) *This answer applies to all of the different red numbers too.
14. Find an expression for the function whose graph is the given curve. (Assume that the points are in the form(x, f(x)).)
The line segments joining the points (3, -5) and (7, 9)
Answer: 7x/2 – 31/2
Domain: [3,7]
The line segments joining the points (3, -3) and (7, 11)
Answer: 7x/2 – 27/2
Domain: [3,7]
The line segments joining the points (1, -4) and (5, -2)
Answer: 1x/2 – 9/2
Domain: [1,5]
15. Find a formula for the described function. A rectangle has perimeter of 16 m. Express the area A of the rectangle as a function of length, L, of one of its sides.
Answer: A = 8L-L^2
Domain: (4,8)
Find a formula for the described function. A rectangle has perimeter of 20 m. Express the area A of the rectangle as a function of length, L, of one of its sides.
Answer: A = 10L – L^2
Domain: (5,10)
Find a formula for the described function. A rectangle has perimeter of 24 m. Express the area A of the rectangle as a function of length, L, of one of its sides.
Answer: A = 12L – L^2
Domain: (6,12)
16. A cell phone plan has a basic charge of $40 a month. The plan includes a 600 free minutes and charges 10 cents for each additional minute of usage. Write the monthly cost C (in dollars) as a function of the number x of minutes used.
C(x) = { 40 if 0 <= x <= 600
{40 + 0.10(x-600) if x>600
A cell phone plan has a basic charge of $45 a month. The plan includes a 600 free minutes and charges 10 cents for each additional minute of usage. Write the monthly cost C (in dollars) as a function of the number x of minutes used.
C(x) = { 45 if 0 <= x <= 600
{45 + 0.10(x-600) if x>600
