Graphing
The name for all of the inputs or x values of a function?
What is the domain?
Write the explicit formula for the sequence: -12, -8, -4, 0, 4, ...
a(n)= -12+ 4(n-1) or a(n)=4n-16
Identify the vertex of the parabola given by y=x2−4x+3.
vertex at (2,−1)
Evaluate: If f(x)=2x, what is f(3)?
8
What is the vertex of the parabola: y=(x−1)2+4
(1, 4)
Another name for the outputs of a function.
What is the range?
Is the square root of 3 rational or irrational?
irrational
Identify the maximum of y=−x2+7.
(0, 7)
The outputs on an exponential graph change using this operation
multiplication
What is the range of the equation: y=2x2+3?
{y | y greater than or equal to three} OR [3, infinity)
The type of line you draw on a graph for this equation: y > -3x + 6
dashed
What is the rate of change between the points (1, 4) and (12, 3)?
slope: -1/11
Find the zeros of x2+5x+6
-2, -3
What is the growth rate in this equation: y=5100(1.04)t?
1.04 growth of 4 percent
What are the solutions to the equation: x2−3x−10=0
x=5 and -2
This is true when a point is NOT a solution to a linear inequality
the point is not in the shaded region
Write the recursive formula for the sequence: -8, 16, -32, 64, ....
a(n)=a(n-1) * -2; a(1) = -8
A projectile follows the path modeled by y=−2x2+8x+1 (units in meters). Find the x-coordinate(s) where the projectile hits the ground.
4.12 seconds
Write a model for this scenario: Sam purchased a car for $32,000. It depreciates at a rate of 7.5% each year.
y=32,000(1-0.075)t ory = 32,000(.925)t
Which graph has a higher maximum? y=−x2+4 or y=−x2+4x+5?
y=-x2+4x+5
The invisible boundary line on an exponential graph that the graph never touches or passes.
asymptote
Word problem: Write an expression that represents this situation. A small aircraft can carry no more than 2500 pounds. The cargo it is carrying consists of leather jackets and backpacks. Each jacket weighs 2 pounds and each backpack weighs 3 pounds. The weight of the pilot is 175 pounds.
175 + 2x + 3y is less than or equal to 2500
What is the vertex form of the equation: y=x2+6x+5
vertex form y=(x+3)2−4
A bacteria culture triples every hour. If you start with 50 bacteria, write an exponential function for the population after t hours and find the population after 5 hours.
P(t)=50⋅3t. After 5 hours: P(5)=12,150
When given a table, how do you know if a function is a quadratic by looking at the outputs?
The outputs have a pattern when you compare their differences two times; constant second difference