Mr. Orchard’s Math 142 WIR
Test 1 Review
Week 3
1. Sketch the graph g(x) = −|x − 3| + 2.
3
2
1
0
-1
-2
-3
-2
-1
0
2. Find the domain of the following functions:
(a) log8 (3 − 9x)
(b) 10
2
√x
x+1
(c) g(x) =



x3
x+1
15
1
2x
−2 ≤ x < 0
x=0
x>0
1
2
3
4
5
6
Mr. Orchard’s Math 142 WIR
Test 1 Review
Week 3
3. Classify the following functions as power, polynomial (state its degree and leading coefficient), rational, exponential, or none of the above.
(a) 19x4
(b) −4 · (2.3)x
(c) 8x5 − 12x2
(d)
√x
x−3
(e)
x
(x−3)2
Mr. Orchard’s Math 142 WIR
Test 1 Review

 x − 5k x < 4
12
x=4
4. y(x) =
 2
x − 4k x > 4
(a) Calculate lim+ y(x) in terms of k.
x→4
(b) Calculate lim− y(x) in terms of k.
x→4
(c) What value of k makes this limit exist?
(d) What is lim y(x) for this value of k?
x→4
(e) Calculate f (4).
(f) Is this function continuous? Why or why not?
Week 3
Mr. Orchard’s Math 142 WIR
Test 1 Review
Week 3
5. A manufacturer sells lunchboxes for $10 each. The manufacturer has a fixed cost of $400
per month, and a cost of $7 per lunchbox.
(a) What is the cost function for the manufacturer, assuming it is linear?
(b) What is the revenue function for the manufacturer, assuming it is linear?
(c) What is the profit function for the manufacturer?
(d) How many lunchboxes must the manufacturer sell in order to break even?
(e) What is the break even cost?
Mr. Orchard’s Math 142 WIR
Test 1 Review
Week 3
6. A couch manufacturer market research team found the demand function for the company
to be D(x) = 3080 − 35x, giving price per couch when x is thousands of couches.
(a) What is the revenue function for the manufacturer?
(b) How many couches should the manufacturer sell in order to maximize revenue?
7. Write the following expression in its simplest form with no negative exponents:
(2x)−2 y 3
x2 z −1
−2
Mr. Orchard’s Math 142 WIR
Test 1 Review
Week 3
8. If we invest $2300 into an account with an annual rate of 5.1% compounded daily, how
much money will be in the account after two and a half years?
9. An account currently has $3800 in it. It has an annual rate of 3.3% compounded continuously. If the account was opened 4 years ago, how much money was put into it at
that time?
10. Solve the following equations for x.
(a)
1
32x
= 92x+1
(b) 6(1.094x+1 ) = 13
(c) log8 64 = x + 3
(d) log2 (25x − 11) + log2 (x + 9) = 2 log2 (5x)
Mr. Orchard’s Math 142 WIR
Test 1 Review
Week 3
11. The following table gives values for f (x).
x
f (x)
1.9
-5.22103
1.99 -5.02092
1.999 -5.00201
2
-5
2.001 -4.99802
2.01 -4.98055
2.1
-4.82301
(a) Fill in the table below to 5 decimal places:
(2)
h
f (2 + h) − f (2) f (2+h)−f
h
−0.1
−0.01
−0.001
0
DNE
0.001
0.01
0.1
(b) Use the table from part (a) to guess the slope of the tangent line of f at (2, −5).
(c) What is the equation for the tangent line of f at (2, −5)?
12. Write the following expressions using only one logarithm: log7 (z +2)−log7 (x)−4 log7 (y).
Mr. Orchard’s Math 142 WIR
Test 1 Review
Week 3
13. How long will it take an investment to triple in value if it is compounded daily at an
annual rate of 8.2%?
14. How long will it take a $500 investment to be worth $600 if it is continuously compounded
at an annual rate of 11%?
15. Account A has an annual rate of 4.7% compounded continuously. Account B has an
annual rate of 4.8% compounded monthly.
(a) What is the effective rate of account A?
(b) What is the effective rate of account B?
(c) Which account is better for your money?
Mr. Orchard’s Math 142 WIR
Test 1 Review
Week 3
16. Use the change of base formula to evaluate log3.3 (102.2) to 3 decimal places.
17. The function M (x) = 12x2 + 18x + 3 gives the number of miles a car can go on x gallons
of gas. What is the average rate of change of this function on the interval [10, 15]? What
are the proper units?
18. A ball is thrown out of a window. It’s distance from the ground can be given by the
function D(t) = −16t2 + 5t + 250 where time t is measured in seconds, and D(t) in feet.
(a) What is the instantaneous velocity at t = 1 second? What are our units?
(b) Find the function that gives the instantaneous velocity of the ball for any time t.
Mr. Orchard’s Math 142 WIR
Test 1 Review
Week 3
19. Below is the function of g(x).
8
6
4
2
0
-2
-4
-2
-1
0
(a) Where is g(x) differentiable? Use interval notation.
(b) Where is g 0 (x) > 0?
1
2
3
4