Mr. Orchard’s Math 142 WIR
Test 1 Review
Week 4
1. The graph of g(x) is the graph of f (x) shifted right by 3, contracted vertically by a
factor of 12 , and shifted down by 3. If f (x) = |x|, what is the formula for g(x)?
2. Find the domain of the following functions:
(a) 55x3 − 3x2 + 22 − 2x−2
√
(b) 2
15−x
(c)
x3 −xπ
ex2
(d)
log(x+9)
x2 −400

 x−9
−4 ≤ x < 5
5≤x<8
(e) f (x) =

log2 (x + 7)
x≥8
1
x−7
Mr. Orchard’s Math 142 WIR
Test 1 Review
Week 4
3. Graph the
 function g(x), where
x < −6
 −8
−9
x = −6
g(x) =

−4x − 28 x > −6
20
15
10
5
0
-5
-10
-15
-20
-20
-15
-10
-5
0
5
10
15
20
Mr. Orchard’s Math 142 WIR
Test 1 Review
Week 4
4. Samantha works for Dear Inside Realty. She earns a base pay of $3,500 per month and
a $1,300 commission for the first 6 houses she sells in the month. For each house after
that, she earns $1,900 in commission. Write a formula for C(x), the amount of money
Samantha makes in a month when she sells x houses.
5. For the quadratic function y = 4x2 − 16x + 15, what are the coordinates of the vertex?
6. Solve the following equation for t:
3(3t−4) 32t = 1
Mr. Orchard’s Math 142 WIR
Test 1 Review
Week 4
7. When the price of a particular brand of laptop is $2,280 per laptop, 10,000 are demanded.
For the demand to be 30,000 laptops, the price must be $1,680 per laptop. Round to
the nearest unit or cent as applicable.
(a) What is the price-demand function for this brand of laptop?
(b) What is the revenue function for this laptop maker?
(c) How many laptops must be sold to maximize revenue?
(d) What is the maximum revenue?
(e) What is the price the manufacturer should charge to reach the maximum revenue?
Mr. Orchard’s Math 142 WIR
Test 1 Review
Week 4
8. A manufacturer of videogame consoles is willing to supply x GameStation 360s when
the price is p = x+2268
. Market research has determined the price-demand function to
5
2528−4x
be p =
. Round to the nearest unit or cent as applicable.
5
(a) What is the equilibrium price for the GameStation 360?
(b) What is the equilibrium quantity for the GameStation 360?
9. $5,000 is invested in a bank account. The account accrues interest at 5% per year. How
much is in the account after 6 years if the account is compounded
(a) annually?
(b) every four months?
(c) continuously?
Mr. Orchard’s Math 142 WIR
Test 1 Review
Week 4
10. The cost function C(x) and the demand function D(x) for a particular commodity are
given below, where x is in thousands of units, C(x) is in thousands of dollars, and D(x)
is price per unit. Round to the nearest unit or cent as applicable.
C(x) = 250x + 5240
D(x) = 4600 − 75x
(a) What is the revenue function for the commodity?
(b) How many units must the company sell to break even?
(c) How many units must the company sell to maximize revenue?
(d) What is the profit when revenue is maximized?
(e) How many units must the company sell to maximize profit?
(f) What is the maximum profit?
Mr. Orchard’s Math 142 WIR
Test 1 Review
Week 4
11. $1,000 is invested in a bank account accruing interest at 6.3% per year compounded
quarterly. How long will it take the account to have $1,800? Round to two decimal
places.
12. Bank account A is compounded continuously at a rate of 5.4% per year. Account B is
compounded semiannually at a rate of 5.7% per year. Find which account is better for
your money by comparing the effective yield rates.
13. Use the properties of logarithm to rewrite the following expression with one logarithm:
4 log9 (z + 7) − 2 log9 (x) +
2
log9 (y − 2)
3
Mr. Orchard’s Math 142 WIR
Test 1 Review
14. Solve the following equations for x:
(a) e(x−2) + 3 = 0
(b) e(x−2) − 3 = 0
(c) log2 (6 − 5x) = 3
(d) log8 (4x − 14) + log8 (x + 7) = 2 log8 (2x)
(e) log2 (12x − 12) = 3 + log2 (x + 5)
Week 4
Mr. Orchard’s Math 142 WIR
Test 1 Review
15. Solve the following equations for x to 4 decimal places:
(a) 4.5(10x ) = 4
(b) 3(2.032x−1 ) = 9
16. Determine the limit (if it exists).
(a) lim 2x(8x − 3)
x→2
x2 −9
2 −5x+6
x
x→3
(b) lim
x2 −1
2
x→−1 x +2x+1
(c) lim
Week 4
Mr. Orchard’s Math 142 WIR
Test 1 Review
Week 4
17. The graph of f (x) is given below.
5
4
3
2
1
0
-1
-1
0
Find the following limits if they exist:
(a) lim f (x)
x→1
(b) lim+ f (x)
x→2
(c) lim− f (x)
x→2
(d) lim f (x)
x→3
1
2
3
4
Mr. Orchard’s Math 142 WIR
Test 1 Review
1
x+2
x < 15
5
√
40 − x x > 15
Determine the following quantities (if they exist).
18. f (x) =
(a) lim+ f (x)
x→15
(b) lim− f (x)
x→15
(c) lim f (x)
x→15
(d) f (15)
Week 4
Mr. Orchard’s Math 142 WIR
Test 1 Review
19. Find the
value of A that makes the following function continuous at x = 3:
 7 − 4x x < 3
A
x=3
g(x) =
 2
x − 14 x > 3
20. Find the average rate of change of f (x) = 4x2 − 1 over the interval [−6, 2].
Week 4
Mr. Orchard’s Math 142 WIR
Test 1 Review
Week 4
21. The cost in dollars of making a particular commodity is given by C(x) = 5000 + 12x +
.05x2 .
(a) Find the average rate of change of C(x) on the interval [100, 101].
(b) Find the instantaneous rate of change of C(x) at x = 100.
22. Find the equation of the tangent line to the function y = 7x − x2 at the point (1, 6).
Mr. Orchard’s Math 142 WIR
Test 1 Review
Week 4
23. Write the limit definition of the derivative for f (x).
24. Use the limit definition of the derivative to find f 0 (x) for the following functions.
(a) f (x) = 6x2 − 20
(b) f (x) =
3
x
(c) f (x) =
√
x+3
Mr. Orchard’s Math 142 WIR
Test 1 Review
Week 4
25. Below is the graph of G(x).
3
2
1
0
-1
-2
-3
-4
-5
-3
-2
-1
0
Where is G(x) differentiable?
26. (a) Use the limit definition to find g 0 (x) when g(x) =
5
.
x−4
(b) Find the equation for the line tangent to g(x at the point x = 5.
1
2