Unit 6
If -1, a, b, c, 11 forms an arithmetic sequence, what is the value of a + b + c?
15
Given the function y = 3 . 2(x+4) -1, what part of the function represents the growth factor?
2
Which of the following properties is illustrated by the following statement?
If ab = 0, then a=0 or b=0 or a=b=0.
Zero Product Property
Determine the discriminant and state the number and type of solutions
2n2 + 3n + 20 = 0
Discriminant = -151
2 complex solutions
State the parent function:
f(x) = 2x
Exponential
Which of the following yields the largest 7th term? For n≥1.
f(n) = 4n + 13
f(n) = -6n + 1
f(n)= 7n - 8
f(n) = 2n + 28
f(n) = 2n + 28
Given the parent function f(x) = 3x list all of the transformations that apply to g(x) given that g(x) = 2 . 3x-4 + 1. Use vocabulary such as: vertical, horizontal, stretch, shrink, shift, translation, reflection, etc.
Vertical stretch by a factor of 2, horizontal shift right 4, and a vertical shift up 1
Factor completely
x4 - 81
(x2 + 9)(x+3)(x-3)
Simplify
i251
-i
State the transformations (in order):
g(x) = -1/5 f(x) + 2
Reflect over x-axis, vertical shrink by a factor of 1/5, shift up 2 units
Write the general term formula for the given sequence:
-8, -3, 2, 7, ...
f(n) = 5n - 13
Gina bought a new laptop computer for $1200. The value of the computer decreases by 40% each year.
What is the computer’s value after 7 years? (Use appropriate rounding)
$33.59
Solve the quadratic equation:
0 = 7(x - 6)2 - 14
x = 6 +/- rad 2
Find the real values of x and y
5x - 13yi = -10 + 2i
x = -2
y = -2/13
State the transformations (in order):
f(x) = -f(x+1) - 2
Shift left 1 unit, reflect about x-axis, shift down 2 units
Write the general term formula for the given sequence:
3, 6, 12, 24, ...
f(n) = 3(2)n-1
Recent smart phone sales have had a growth rate of 24.5% from 2012 to 2013. If the growth rate for smart phones remains at 24.5% each year, how many smart phones will be sold in 2017 if 567 million phones were sold in 2013? (Use appropriate rounding)
1,362,261,443 phones
Solve
0 = x2 + 14x - 7
x = -7 +/- rad 14
Perform the indicated operation and express the result in a + bi form.
(6 + 8i)(-2 + 6i)
-60 + 20i
Solve the system of equations using substitution:
y = x2 + 3x + 2
2x + y = -4
(-2, 0)
(-3, 2)
A new exhibit is scheduled to open at a local museum. Museum officials expect that 9000 people will visit the exhibit in its first week, and the number of visitors will drop by 10 people per week after the first week during the first 6 months. Find the number of visitors expected in the exhibit’s 11th week.
f(11) = 8,900 vistors
State the range of the function:
f(x) = -(1/2)(x+3) + 1
Range: (- infinity, 1)
Convert into vertex form, then identify the vertex
y = 3x2 + 24x + 40
(-4, -8)
Divide and express in a + bi form
4+3i/5-2i
23i/29
Solve the system of equations by graphing
y = x2 - 1
y = 2x - 1
(0, -1)
(2, 3)