College Algebra Final Exam Review
questions with solutions
Find the difference quotient, (f(x+h) - f(x))/h, h does not equal 0, for each of the following
functions.
a) f(x) = x^2 - x - 2
b) 3x^2 - 2x + 6 - answersa) 2x + h - 1
b) 6x + 3h - 2
Determine algebraically whether the follwoing functions are even, odd or neither.
a) f(x) = 3x^4 - 2x^2
b) g(x) = 2x^5 + x
c) h(x) = 7x^2 + 5x - 1 - answersa) Even
b) odd
c) neither
let f(x) = x^2 - 9x and g(x) = 2x + 3, Find each of the following.
a) (f + g)(x)
b) (f - g)(x)
c) (fg)(x)
d) (f/g)(x)
e) (g(f(x))
f) (f(g(x)) - answersa) x^2 - 7x + 3
b) x^2 - 11x -3
c) 2x^3 - 15x^2 - 27x
d) (x^2 - 9x) / (2x + 3)
e) 2x^2 - 18x + 3
f) 4x^2 - 6x - 18
The formula S = 7/2 Sqrt:2D can be used to approximate the speed S, in miles per hour,
of a car that has left skid marks in length D, in feet. How far will a car skid at 70 mph?
Round to 1 decimal - answers200 ft.
The function f(x) = 27x^1/3 models the number of plants species, f(x), on an island in
terms of the area, x, in square miles. What is the area of an island that has 54 species
of plants? - answers8 Square Miles
A company charting it's profits notices that the relationship between the number of units
sold, x, and the profit, P, is linear.
, a) If 200 units sold results in $3100 profit and 250 units sold results in $6000 profit, write
the profit function for this company.
b) State the slope and interpret it in the context of the problem. - answersa) P(x) = 58x -
8500
b) The slope if 58. The profit increases at a rate of $58 for each unit sold.
A certain commodity has fixed costs of $1500 with a variable cost per unit of $22. The
commodity is sold for $52 per unit.
a) Write the cost function
b) write the revenue function
c) write the profit function
d) find the break-even point - answersa) cost : C(x) = 22x + 1500
b) Revenue : R(x) = 52x
c) Profit : P(x) = 30x - 1500
d) Break - Even Point : 50 Units
Find the Augmented matrix of the corresponding linear system.
a) Volunteers X,Y and Z offered to stuff 864 envelopes with newsletters for a charity.
Volunteer X could assemble 170 per hour, volunteer Y, 121 per hour, Z 146 per hour.
They worked a total of 6 hours. The sum of the number of hours that volunteers Y and Z
spent was twice what volunteer X spent. How long did each of them work?
b) Ron attends a cocktail party. He wants to limit his food intake to 133 g protein, 120 g
fat, and 165 g carbs. According to the health conscious hostess, the marinated
mushroom caps have 3 g protein, 5 g fat, and 9 g carbs; the spicy meatballs have 14 g
protein, 7 g fat, and 15 g carbs; and the deviled eggs have 13 g protein, 15 g fat, and 6
g carbs. How mayn of each snack can he eat to obtain his goal - answersa) 1 1 1 6
-2 1 1 0
170 121 146 864
b) 3 14 13 133
5 7 15 120
9 15 6 165
solve 2x^2 + 16x + 26 = 0 - answersx = -4 +- sqrt3
A football is thrown vertically upward from the top of a building 80 feet tall with the initial
velocity of 80 feet per second. The distance d (in feet) of the ball from the ground after t
seconds is d(t) = 800 + 80t - 16t^2. What is the max height of the ball? After how many
secnds will the ball hit the ground? - answersmax height : 900 feet, it will take 10
seconds for the ball to hit the ground
questions with solutions
Find the difference quotient, (f(x+h) - f(x))/h, h does not equal 0, for each of the following
functions.
a) f(x) = x^2 - x - 2
b) 3x^2 - 2x + 6 - answersa) 2x + h - 1
b) 6x + 3h - 2
Determine algebraically whether the follwoing functions are even, odd or neither.
a) f(x) = 3x^4 - 2x^2
b) g(x) = 2x^5 + x
c) h(x) = 7x^2 + 5x - 1 - answersa) Even
b) odd
c) neither
let f(x) = x^2 - 9x and g(x) = 2x + 3, Find each of the following.
a) (f + g)(x)
b) (f - g)(x)
c) (fg)(x)
d) (f/g)(x)
e) (g(f(x))
f) (f(g(x)) - answersa) x^2 - 7x + 3
b) x^2 - 11x -3
c) 2x^3 - 15x^2 - 27x
d) (x^2 - 9x) / (2x + 3)
e) 2x^2 - 18x + 3
f) 4x^2 - 6x - 18
The formula S = 7/2 Sqrt:2D can be used to approximate the speed S, in miles per hour,
of a car that has left skid marks in length D, in feet. How far will a car skid at 70 mph?
Round to 1 decimal - answers200 ft.
The function f(x) = 27x^1/3 models the number of plants species, f(x), on an island in
terms of the area, x, in square miles. What is the area of an island that has 54 species
of plants? - answers8 Square Miles
A company charting it's profits notices that the relationship between the number of units
sold, x, and the profit, P, is linear.
, a) If 200 units sold results in $3100 profit and 250 units sold results in $6000 profit, write
the profit function for this company.
b) State the slope and interpret it in the context of the problem. - answersa) P(x) = 58x -
8500
b) The slope if 58. The profit increases at a rate of $58 for each unit sold.
A certain commodity has fixed costs of $1500 with a variable cost per unit of $22. The
commodity is sold for $52 per unit.
a) Write the cost function
b) write the revenue function
c) write the profit function
d) find the break-even point - answersa) cost : C(x) = 22x + 1500
b) Revenue : R(x) = 52x
c) Profit : P(x) = 30x - 1500
d) Break - Even Point : 50 Units
Find the Augmented matrix of the corresponding linear system.
a) Volunteers X,Y and Z offered to stuff 864 envelopes with newsletters for a charity.
Volunteer X could assemble 170 per hour, volunteer Y, 121 per hour, Z 146 per hour.
They worked a total of 6 hours. The sum of the number of hours that volunteers Y and Z
spent was twice what volunteer X spent. How long did each of them work?
b) Ron attends a cocktail party. He wants to limit his food intake to 133 g protein, 120 g
fat, and 165 g carbs. According to the health conscious hostess, the marinated
mushroom caps have 3 g protein, 5 g fat, and 9 g carbs; the spicy meatballs have 14 g
protein, 7 g fat, and 15 g carbs; and the deviled eggs have 13 g protein, 15 g fat, and 6
g carbs. How mayn of each snack can he eat to obtain his goal - answersa) 1 1 1 6
-2 1 1 0
170 121 146 864
b) 3 14 13 133
5 7 15 120
9 15 6 165
solve 2x^2 + 16x + 26 = 0 - answersx = -4 +- sqrt3
A football is thrown vertically upward from the top of a building 80 feet tall with the initial
velocity of 80 feet per second. The distance d (in feet) of the ball from the ground after t
seconds is d(t) = 800 + 80t - 16t^2. What is the max height of the ball? After how many
secnds will the ball hit the ground? - answersmax height : 900 feet, it will take 10
seconds for the ball to hit the ground
