Algebra 1 Math Final Study Guide
g(r) = −1−7(r) g(6) = ?
-43
g(x) = −3x−8 g( ? ) = 10
-6
r(m) models the average monthly rainfall (in millimeters) in Tanzania for the years 1900-2009 as a function of the month number m. Month Rainfall (millimeters) 1 145 2 135.8 3 179.1 4 171 5 64.8 6 12.6 7 8.4 8 8.9 9 15.7 10 29.5 11 83.8 12 142.6 1. Which number is more appropriate for the domain of r? A.) Integers B.) Real Numbers 2. Whats the appropriate domain? A.) 1 ≤ m ≤ 12 B.) 8.4 ≤ m ≤ 179.1 C.) 1900 ≤ m ≤ 2009 D.) 0 ≤ m ≤ 179.1
1. A 2. A
The exponential function f, represented in the table, can be written as f(x)= a⋅b^x x f(x) 0 15 1 9
15 X 9/15^x
What is the inverse of the function h(x)= 3/2 (x-11)? h-1(x)= ?
2/3x + 11
There were 230,600 jobs available in the field of radiology in the year 2014. Each year, that number is expected to grow by 0.9%. Write a function that gives the expected number j(t) of jobs in radiology t years from the year 2014. j(t)=?
230600 X (1.009)^t
√52x^4
2x^2 √13
Factoring Difference of Squares: 3x^2 - 147
3(x+7) (x-7)
Multiplying Difference of squares: (7+x) (7-x)
49-x^2
Multiplying Perfect Squares: (2x-3) (2x-3)
4x^2-12x+9
Two videos on viewtube.com were recently uploaded. One is a playful kitten video and the other is a laughing baby video. The kitten video had 10 views by the end of the first minute after it was uploaded, and the cumulative number of views increases by 50 views by the end of each additional minute. The baby video had 3 views by the end of the first minute after it was uploaded, and the cumulative number of views increases by a factor of approximately 3.5 by the end of each additional minute. By the end of which minute will the baby video's cumulative number of views first exceed the kitten video's cumulative number of views?
5
remove the perfect squares: √125
5 √5
A car sells for $5000 and loses 1/10 of its value each year. Write a function that gives the car's value, V(t), t years after it is sold. V(t)=?
5000 X 9/10^t
Multiply Binomials: a polynomial in standard form (5a+2) (a+4)
5a^2+22a+8
6 to the -6 power over 6 to the -5 power 6^-6/6^-5
6^-1
h(x)= 4/x-5 What is the domain of h? A.) All real values of x such that x does not = 4 B.) All real values of x such that x≥ 4 C.) All real values of x such that x does not = 5 D.) All real values of x such that x ≤ 5 E.) All real values of x
C
Connecting exponential graphs with contexts (exercise #27)
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Domain and Range from Graph (exercise #6)
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Functions inputs and outputs: graphs (exercise 3)
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Graphing exponential growth and decay (exercise 24)
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Grouping: -8x^2 - 15x + 2
(-8x+1) (x+2)
Factoring Perfect Squares: 25 + 70x + 49x^2
(5+7x) (5+7x) or (5+7x)^2
x f(x) -5 0 -4 2 -3 6 -2 7 -1 5 0 3 1 0 2 -3 3 -5 4 -1 5 2 What is the Average rate of change of f over the interval [3,4]?
-1-(-5) /4-3 = 4
"Princess Tower" in Dubai is considered the world's tallest residential building, towering to 101 floors! T(n) models the number of tenants living on floor n of the tower. What does the statement T(60)>T(10)+T(30) mean? Choose 1 answer: A.) The number of floors with 60 tenants is greater than the number of floors with either 101 or 30 tenants. B.) There are more tenants on floor 60 than there are tenants on floors 101 and 30 combined. C.) The height of floor 60 is greater than the sum of the heights of floors 101 and 30.
B
Shota invests \$1000 in a certificate of deposit that earns interest. The investment's value is multiplied by 1.02 each year. Which expression gives the investment's value after 5 years? A.) 1000 + (1+1.02)^5 B.) 1000⋅1.02^5 C.) 1000⋅(1+1.02)^5 D.) 1000 + 1.02^5
B
Which 2 expressions are equivalent to 2^5/6^5? A.) 1/3 B.) 3^-5 C.) (-4)^-5 D.) 2^5 ⋅6^−5 (^=an exponent)
B,D
Andrei has a glass tank that he would like to fill with marbles and water. W(m) models the amount of water Andrei needs (in liters) if he uses m marbles. m 10 32 68 W(m) 36.5 28.8 16.2 When does the amount of water decrease faster? A.) Between 10 marbles and 32 marbles B.) Between 32 marbles and 68 marbles C.) The necessary amount of water decreases at the same rate over both intervals
C
Select the equivalent expression: (a ^−7⋅b ^−2) ^−9= ? A.) b^18/a^63 B.) a^63/ b^18 C.) a^63 ⋅ b^18 (^ = an exponent right after)
C
Time(months) Milkshakes Sold 1 259 4 380 7 501 10 622 13 744 Linear or Exponential growth? (Linear=straight line, Exponential=curved line in a graph)
Linear
x 15 16 17 18 y 10 20 40 70 Linear, Exponential or Neither?
Neither
For a given input value b, the function f outputs a value a to satisfy the following equation: 4a + 7b = -52 Write a formula for f(b) in terms of b. f(b)= ?
f(b)= -13 - 7/4b
Factoring Quadratics: A rectangle has an area of x^2 - 11x + 30 and a length of x - 5. What expression represents the width of the rectangle?
x-6
√24b^3⋅√40b^2⋅√b^2
√960b^7
Increasing and Decreasing Intervals (exercise #9)
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