Function Basics
What is the mathematical term for a relationship between two variables, where one variable depends on the other?
Function
What is the standard notation for a function?
f(x)
What is the slope-intercept form of a linear equation?
y = mx + b
What is a linear function?
A function whose graph is a straight line.
A phone plan costs $20 per month plus $0.10 per minute. Write a function to model the monthly cost.
C(m) = 20 + 0.10m
What is the vertical line test used for?
To determine if a graph represents a function.
If f(x) = 2x + 1, what is the value of f(3)?
7
What is the point-slope form of a linear equation?
y - y₁ = m(x - x₁)
What is a quadratic function?
A function whose graph is a parabola.
A ball is thrown upward from a height of 6 feet with an initial velocity of 32 feet per second. Write a function to model the height of the ball after t seconds.
h(t) = -16t² + 32t + 6
What is the set of all inputs values of a function called?
Domain
Given the function g(x) = x^2 - 4, what is the value of g(-2)?
0
What is the standard form of a quadratic equation?
ax² + bx + c = 0
What is an exponential function?
A function of the form f(x) = a^x, where a is a constant.
A store sells t-shirts for $15 each. Write a function to represent the total cost of t t-shirts.
C(t) = 15t
What is the set of all outputs values of a function called?
Range
What is function composition?
Applying one function to the result of another function, denoted as (f ∘ g)(x) = f(g(x))
What is the vertex form of a quadratic equation?
y = a(x - h)² + k
What is a logarithmic function?
The inverse of an exponential function.
A car depreciates in value by 15% each year. If the initial value of the car is $20,000, write a function to model the value of the car after t years.
V(t) = 20000(0.85)^t
What is the difference between independent and dependent variable?
The independent variable is the input, while the dependent variable is the output.
If f(x) = 4x - 2^2, what is the value of x if f(3)?
8
What is the parent function of a quadratic function?
f(x) = x²
What is a rational function?
A function that can be expressed as the quotient of two polynomial functions.
A bacteria culture doubles in size every hour. If the initial population is 100 bacteria, write a function to model the population after t hours.
P(t) = 100 * 2^t