Linear
The sequence that involves adding the same number each time to get to the next term.
Also related to linear functions.
What is arithmetic sequences?
The parameter that lets you know if an exponential function is a growth or decay.
What is the base?
These are words that mean the same thing as finding the solutions of a quadratic equation.
What are roots, x-intercepts, and zeros?
What type of function is
y = 2x + 5
Exponential
Solve the equation for x:
12 - (4x + 5) = 7 - 4x
The function p(x) = x + 5 has a special point located at (0, 5) .
What is the y-intercept?
In the equation y = a(b)x, what does the a represent?
What is the initial value.
Rewrite f(x) in factored form.
f(x) = (x+5)(x+1) or (x+1)(x+5)
Lanae filled up her gas tank on the way home from work. She uses about 1.6 gallons each day. After 3 days, she has 21.3 gallons of gas left in her gas tank.
Write an equation to represent the number of gallons of gas, g, in her tank after d days.
(Hint: look at what you're given!)
y = 1.6x + 16.5
or
g = 1.6d + 6.5
Let a(n) be the sequence: 7, 3, -1, -5,....
Write a rule for the following sequence.
(Hint: an = ?)
an = 11 - 4n
or -4n + 11.
In the equation
-2x - y = 8,
these are the coordinates of the y-intercept.
What is (0, -8)
Tawana and Trevon are trying to buy an antique baseball card. The function v(t) = 500(1.13)x represents the value, in dollars, of the baseball card x years since 1995.
a) What is the percent of growth each year?
b) How much will the card be worth in 2022?
a) What is 13%
b) What is $13,554.64
Let h(x) = -6t2 + 3t + 18 represent the height, in feet, of the ball after being in the air for t seconds.
Q: What is the height of the ball after 1 second?
A: 15 feet
Let p(x) = 2(3)x-3 + 2
Let q(x) = -2(3)x-3 + 4
What transformations get you from p(x) to q(x)?
Reflection across the x-axis and a vertical shift/translation up two units.
Solve the radical equation, and don't forget to check for opps!
What is no solution!
The graph of the linear function f(x) has an x-intercept of (-2,0) and a y-intercept of (0,3).
The graph of linear function g(x) is defined by the equation
y = 0.8x-2
Fill in the blanks below:
"The y-intercept of the graph of f(x) is __________ the y-intercept of the graph of g(x). The slope of the graph of f(x) is ___________ the slope of the graph of g(x)."
What is greater than/higher than, smaller than/less than.
Alexis put $75 in a new bank account at the end of 2012. Each year thereafter, the total balance in the account tripled from the balance one year prior.
a) Write an equation to represent the balance of the account y, x years after her initial deposit.
b) Find the balance of the account at the end of 2015.
a) y = 75(3)x
b) $2,025
Let f(x) = x2 + 10x + 5.
a) What are the roots of the equation?
b) What is the equivalent form of f(x) in vertex form?
a) {-9.47, -.53}
b) f(x) = (x + 5)2 - 20
Let a(x) = 4x2 + 9x - 13
Let b(x) = -2.5x + 3
Let c(x) = 4(1.5)x - 1 + 2.
This equation has the greatest y-intercept.
What is c(x)?
James asked the class what their shoe sizes are. Here are his results:
5, 5, 9, 9, 7, 6, 11, 12, 13, 7, 7
Create a box and whisker plot of the data set.
*check*
Let f(x) be the function defined by
f(x) = 2x + 5.
a) If g(x) = f(x) - 2, what is the equation of g(x)?
b) If h(x) = f(x-2), what is the equation of h(x)?
a) g(x) = 2x + 3 (down 2)
b) h(x) = 2x + 1 (right 2)
The value of a boat after x years is given by the following ordered pairs:
(0, 120000), (1, 108000), (2, 97200), (3, 87480)
Write an exponential function representing the value, y, of a boat when it is x years old.
What is y = 120,000(0.9)x
A volleyball is served from a height of 3 feet, then 0.75 seconds later reaches a maximum height of 12 feet. Assuming the ball continues on its pathway, write an equation to represent the height, h, of the ball, t seconds after it was served.
(Hint: use vertex form and use the y-intercept to find "a")
An outdoor music festival began in 2015 with 25,000 attendants. Since then, the attendance has decreased by 6% each year.
a) What type of function models this scenario?
b) Write an equation to represent the attendance, y, at the music festival, x years after 2015.
c) Approximately how many people will attend the festival in 2022?
a) Exponential
b) y = 25,000(0.94)x
c) about 16,212 people
Ivy went to the store and spent $45 on 3 shirts and 2 pairs of jeans. The next day, she went back and spent $21 on one shirt and one pair of jeans.
Using this information, how much does one pair of jeans cost?
What is $18?