Math 1101 Test 3 Review
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Simplify.
1) (x3 y6 )(x2 y4 )
2)
15x8 y4
5x2 y
Simplify. Write the answer using positive exponents only.
3) (x-3 y4 )-2
Evaluate the piecewise function at the given value of the independent variable.
4)
x+3
if x > -5
f(x) =
-(x + 3) if x ≤ -5
Determine f(-6).
1
What restrictions are on the domain of the function?
x2 + 3x
5) f(x) =
x2 - 5x - 24
Given functions f and g, perform the indicated operations.
6) f(x) = 4x - 9,
g(x) = 7x - 3
Find f - g.
7) f(x) = 8x + 5,
Find fg.
g(x) = 4x + 1
For the given functions f and g , find the indicated composition.
8) f(x) = 7x + 9,
g(x) = 2x - 1
(f∘g)(x)
2 3x
9) Let f(x) = 5( ) . What is f(-1) ?
3
2
10) A particular cell phone depreciates in value at the rate of 25%. Write a function that could be used to determine
the value of a phone which had an inital value of $875 after t years..
.
Solve the problem.
11) What amount if appreciated for 10 years in an account that earns 7% interest, compounded quarterly will
become $1967.15.
Find the amount that will be in an account, given the stated conditions.
12) P = $680, t = 17, r = 9% compounded continuously
Graph the function.
13) f(x) = 2 x
6
y
4
2
-6
-4
-2
2
4
6 x
-2
-4
-6
3
Convert to an exponential equation.
14) log6 216 = t
Find the value of the expression.
1
15) log
5 625
16) log 32
2
Find the following using a calculator. Round to four decimal places.
17) ln 281
18) Write as a single logarithm log 30 + log 6 - 3 log 2
Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places
19) log2 12
4
20) Which function contains the points (2, -75) and (4, -1875)
Solve the exponential equation.
21) 8 2x = 8 10
22) 6 x+4 = 4 x
Round your answer to the nearest thousandth.
Solve the logarithmic equation.
23) log x = 2
5
24) ln(3x - 4) = ln 20 - ln (x - 5)
25) log (x + 10) - log (x + 4) = log x
5
Answer Key
Testname: 1101 TEST 3 REVIEW 2
1) x5 y10
2) 3x6 y3
3)
x6
y8
4) 3
5) x = 8
6) -3x - 6
7) 32x2 + 28x + 5
8) 14x + 2
135
9)
8
10) f(t) = 875(.75)t
11) $982.79
12) $3140.36
13)
6
y
4
2
-6
-4
-2
2
4
6 x
-2
-4
-6
14) 6 t = 216
15) -4
16) 5
17) 5.6384
18) log 20
19) 3.5850
20) f(x) = -3 (5)x
21) 5
22) -17.676
23) 25
19
24)
3
25) 2
6