Linear Functions
What is the equation of a linear function?
y = mx + b
What is a nonlinear function?
A function whose graph is not a straight line.
What does it mean to analyze a function?
To study its behavior, such as finding its domain, range, intercepts, and symmetry.
Write an equation to represent the total cost (C) of buying n tickets that cost $12 each.
C = 12n
What is the term for the value of "b" in the equation y = mx + b?
Y-intercept
What is the slope-intercept form of a linear function?
y = mx + b, where m is the slope and b is the y-intercept.
Give an example of a nonlinear function.
exponential function: y = 2^x.
How do you find the domain of a function?
The set of all possible input values (x-values).
Create an equation to represent the area (A) of a rectangle with length L and width W.
A = LW
What is the term for the steepness of a line in a linear function?
Slope
What does the slope of a linear function represent?
The rate of change or how steep the line is.
What are the key differences between linear and nonlinear functions?
Linear functions have a constant rate of change (slope), while nonlinear functions do not. Nonlinear functions may have curves or other shapes in their graphs.
How do you find the range of a function?
The set of all possible output values (y-values).
Write an equation to represent the relationship between x and y if y is 3 times the value of x
y = 3x
What do we call the form of a linear equation that explicitly shows the slope and y-intercept?
Slope-intercept form
How do you find the slope of a line given two points?
(y2 - y1) / (x2 - x1)
Why is it called a "nonlinear" function?
Because the relationship between x and y is not described by a straight line.
How do you determine if a function is increasing, decreasing, or constant?
By analyzing the slope of the function. If the slope is positive, the function is increasing. If the slope is negative, the function is decreasing. If the slope is zero, the function is constant.
Create an equation to represent the distance (d) traveled by a car moving at a speed of 50 mph for t hours.
d = 50t
What is the term for the value of "m" in the equation y = mx + b?
Slope