Linear Functions
Write the equation of a linear function.
Anything in the form: f(x)=ax+b
Write the equation of a quadratic function.
Anything in the form: f(x)=ax2+bx+c
f(x)=5x-2
g(x) is the translation of f(x) up two units.
What is the equation of g(x)?
g(x)=5x
Model the following using a function; define your variables:
Brenda saved up seventy dollars this summer and her mom gives her ten dollars every week.
f(x)=10x+70 where x=weeks and f(x)=Brenda's $$$
What American major league sports franchise holds the record for most championships won in its respective sport?
New York Yankees (27 World Series championships)
Describe the graph of a linear function.
A straight line.
Describe the graph of a quadratic function.
A parabola (U-shaped)
g(x)=-3f(x-3) is a transformation of f(x)=x. Describe any transformations or translations that happened to f(x).
f(x) was translated three units to the right, vertically stretched by a factor of 3 and reflected about the x-axis.
Sketch a graph representing the following:
Andrea, Marcus and Alfie race each other. Andrea starts off sprinting, then slows down over the course of the rest of the race. Marcus runs at a steady pace throughout. Alfie starts off jogging then continuously speeds up throughout the race.
Andrea should be represented by something that looks like a radical function. Marcus should be represented using a straight line with a positive slope. Alfie should be represented using something like an exponential function.
She is the first woman named in the Bible, but is only mentioned twice in its first book.
Eve
What is the domain of a linear function?
The domain is all real numbers
Classify the following function: x3+x2
Cubic function
The vertex of a parabola is on the point (-2, 5). If the parabola is reflected about the y-axis, where will the new vertex be?
(2, 5)
Cecil's drive to visit his grandparents is graphed with the x-axis representing the time since Cecil left his house in hours and the y-axis representing the distance he has traveled in minutes. What would it mean if the graph had a slope of 25 from 0<x<1, then a slope of 50 from 1<x<2.5?
Cecil drove on local roads for an hour, going 25 mph, then probably got on a highway and sped up to 50 mph.
This nation was an ally to the American colonies during the Revolutionary War.
France
If f(x)=(3/4)x-5, what is f(12)?
f(12)=4
Graph the function:
h(x) = 3 |x + 2| – 4
(Allow 30 extra second)
See boards
n(x) is a transformation of m(x), where n(x) = -3m(x-2) + 6. Describe the order of transformations occurring from m(x) to n(x).
Translate horizontally two units to the right, then dilate by a factor of 3/reflect about the x-axis, then translate vertically six units up.
Sketch a graph representing the following:
Andrea, Marcus and Alfie race each other. Andrea starts off sprinting, then slows down over the course of the rest of the race. Marcus runs at a steady pace throughout. Alfie starts off jogging then continuously speeds up throughout the race.
Andrea should be represented by something that looks like a radical function. Marcus should be represented using a straight line with a positive slope. Alfie should be represented using something like an exponential function.
This is the most streamed song ever on Spotify (as of 4/14/20)
"Shape of You" by Ed Sheeran
Write the equation of a linear function, then graph this function. (Allow 30 extra seconds)
Answers will vary
Write the equation of an exponential function, then sketch a graph of it.
See boards
g(x)=x is translated up three units, to the right one unit, then horizontally compressed by a factor of 1/3. What is the equation of g'(x)?
g'(x)=(3x-1)+3
The rate of rainfall (in inches per hour) during a rainstorm can be modeled by the function r(t) = –0.5 |t – 1| + 0.5, where t is the time in hours since the beginning of the storm. In how many hours will the rainfall stop?
In 2 hours
What film won the Academy Award for Best Picture in 2020?
Parasite