U6 L3
Evaluating Function Notation
U6 L3
Interpreting piecewise, time-distance, and time-velocity
Graphs
Piecewise:
Time-Distance:
Time-velocity:
U6 L4
Meaning of the Slope in Context
U6 L4
Meaning of the y-intercept in context
U6 L4
How many points make up the graph of a Linear equation?
U6 L5
Increasing/
Decreasing Graphs
Increasing:
Decreasing:
U6 L5
4 possible slopes
give a example to all of them
U6 L3
Evaluating Function Notation: In this lesson, you will learn how to evaluate functions using function notation. For example, if you have a function f(x) = 2x + 3, you can plug in a value for x, such as f(4), to find the corresponding y-value.
Piecewise: In a piecewise function, different rules or equations are used to define the function for different intervals or regions. For example, a piecewise function f(x) could be defined as f(x) = x^2 if x is less than or equal to 0, and f(x) = 2x + 1 if x is greater than 0.
Time-Distance: Time-Distance graphs show the relationship between the time it takes to travel a certain distance. The x-axis represents time, and the y-axis represents distance. A linear Time-Distance graph would have a constant slope, indicating a constant speed.
Time-Velocity: Time-Velocity graphs show the relationship between the time and velocity of an object. The x-axis represents time, and the y-axis represents velocity. The slope of a Time-Velocity graph represents acceleration, with a positive slope indicating a increasing velocity and negative slope indicating decreasing velocity.
U6 L4
Meaning of the Slope in Context: In the context of a linear equation, the slope represents the rate of change or the steepness of a line. For example, if a linear equation represents the relationship between a person's age and their height, the slope would represent the amount their height changes for each year of age.
Meaning of the y-intercept in context: In the context of a linear equation, the y-intercept represents the value of the dependent variable (y) when the independent variable (x) is zero. For example, in the equation y = mx + b, the y-intercept, represented as (0, b), would give the starting value or initial condition of the scenario being modeled.
U6 L4
How many points make up the graph of a Linear equation: A linear equation represents a straight line on a graph. A linear equation will have exactly two points that make up the graph, as it only takes two points to determine a line.
U6 L5
Increasing: An increasing graph shows a positive slope, where the y-values increase as the x-values increase. The line or curve on the graph generally moves upward from left to right.
Decreasing: A decreasing graph shows a negative slope, where the y-values decrease as the x-values increase. The line or curve on the graph generally moves downward from left to right.
U6 L5
Four possible slopes: The four possible slopes of a linear equation are positive slope, negative slope, zero slope (horizontal line), and undefined slope (vertical line).
Example:
- Positive slope: y = 2x + 1, where the line increases as x increases.
- Negative slope: y = -3x + 2, where the line decreases as x increases.
- Zero slope: y = 4, where the line is horizontal and does not change as x increases.
- Undefined slope: x = 5, where the line is vertical and does not change as y increases.