Function Notation and Properties
What do we call the set of all possible input values for a function?
Domain
What kind of transformation moves a graph vertically?
Vertical Translation
What are the solutions to the equation x^2 − 9 = 0?
x=3 and x=−3
What does the inverse of a function do to the original input?
Reverses The Operation
What type of function best models a constant rate of change?
Linear Function
What is the value of f(4) if f(x) = 17x + 13?
81
What is the equation of the graph that results from reflecting f(x) = x^2 over the x-axis?
f(x)=−x^2
What is the solution to the equation 4x + 7 = 12 - 6x?
0.5
What is the inverse of the function f(x)=3x+2?
f^−1(x) = (x−2)/3
What kind of growth is typically modeled by an exponential function?
Rapid Or Exponential Growth
What type of symmetry does an even function have?
Symmetry About The Y-Axis
What year was Ada Lovelace born?
1815
What is the solution set for the inequality 2x−3>52x - 3 > 5?
x>4
What test must a function pass to have an inverse?
Horizontal Line Test
What number am I thinking of between 1 and 10,000,000?
392, 407
What condition must a relation satisfy to be considered a function?
Each Input Has One Output
What transformations are applied to f(x) to get −2f(x−3)+5?
Reflect over x-axis, vertical stretch by 2, shift right 3, up 5
What is the solution to the equation (x+2)/(x−1)=3?
x = 5/2
What is the total number of letters when you combine the last names of all Grade 11 and 12 math teachers this year?
41
In what kind of situation would a rational function be the best model?
Modeling Rates With Restrictions (e.g., Speed vs. Time With Asymptotes)
What is the range of the function f(x) = x^2 − 4x + 7?
y≥3
How do you write the transformed function that reflects f(x) over the y-axis and shifts it 4 units to the right?
f(-x + 4) or f(−(x−4))
What are the points of intersection for the system y=2x+1 and y=x^2?
x=−1 and x=2; points: (−1, −1) and (2, 5)
Why doesn’t the function f(x)=x2f(x) = x^2 have an inverse over all real numbers?
It Fails The Horizontal Line Test (Not One-To-One)
How would you write a function to model a population that doubles every 5 years?
P(t)=P^0 ⋅ 2^t/5