All Flashcards
What is a function model?
A mathematical representation of a real-world situation.
What is the slope in a linear function?
The rate of change, denoted as 'm' in y = mx + b.
What is the y-intercept in a linear function?
The starting point of the function, denoted as 'b' in y = mx + b.
What is a quadratic function?
A function of the form y = ax² + bx + c, used for situations with a changing rate of change.
What are polynomial functions?
Functions with multiple terms, general form: y = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₁x + a₀.
What are piecewise functions?
Functions defined differently over different intervals of their domain.
What are domain restrictions?
Limits on the x values based on math, context, or extreme data.
What are range restrictions?
Limits on the y values, like rounding or setting a minimum.
What is the degree of a polynomial?
The highest power of x in the polynomial.
What is the significance of the y-intercept?
The point where the function intersects the y-axis (x=0).
How do you find the linear model given two data points?
- Calculate the slope (m). 2. Use one point and the slope to find the y-intercept (b). 3. Write the equation y = mx + b.
How do you determine the domain restriction for y = 1/x?
Recognize that division by zero is undefined, therefore x ≠ 0.
How do you determine the fixed cost from the cost function C(x) = 0.1x² + 5x + 100?
Evaluate C(0) to find the cost when no items are produced. In this case, C(0) = 100.
How do you find the value of a piecewise function at a specific point?
Determine which interval the point falls into, then use the corresponding equation for that interval.
What is the general form of a linear function?
What is the general form of a quadratic function?
What is the general form of a polynomial function?
How do you calculate the slope (m) given two points (x₁, y₁) and (x₂, y₂)?