U6 L5
Linear functions: How do you find slope from a table?
U6 L6
Linear functions: How do you know the y-intercept from a table?
U6 L7
Linear OR
NonLinear Functions
How to tell from a table:
How to tell from a graph:
How to tell from an equation:
U6 L7
Different forms of Linear Equations
Standard Form:
Point-Slope Form:
Slope-Intercept Form:
U7 L7
How do we change from one form to the other?
U6 L8
Compare Linear Functions
Rate of change:
y-intercept:
U6 L9
Linear Functions
Domain/Range
Domain:
Range:
Inequality Notation:
Interval Notation:
U6 L9
Linear Functions
End Behavior
give all of them examples
U6 L5: To find the slope from a table, select two points on the table and calculate the change in the y-values divided by the change in the corresponding x-values.
U6 L6: To determine the y-intercept from a table, find the value of the dependent variable (y) when the independent variable (x) is equal to zero.
U6 L7: To tell if a function is linear or nonlinear from a table, check if the differences in the y-values are the same for each corresponding x-value. If they are, the function is linear. If not, it is nonlinear. From a graph, a linear function will have a straight line, while a nonlinear function will have a curved line. From an equation, a linear function has a degree of 1, while a nonlinear function has a degree greater than 1.
U6 L7: Different forms of linear equations include standard form (Ax + By = C), point-slope form (y - y1 = m(x - x1)), and slope-intercept form (y = mx + b).
U7 L7: To change from one form of a linear equation to another, you can use algebraic manipulations to rewrite the equation. For example, to change from standard form to slope-intercept form, solve for y in terms of x. To change from slope-intercept form to point-slope form, rearrange the equation to isolate y on one side.
U6 L8: The rate of change in a linear function represents how the dependent variable (y) changes for a unit increase in the independent variable (x). It can be calculated as the slope of the line. The y-intercept represents the value of the dependent variable when the independent variable is equal to zero.
U6 L9: The domain of a linear function is the set of all possible input values (x-values) for which the function is defined. The range is the set of all possible output values (y-values). Inequality notation represents the domain and range using inequality symbols, while interval notation represents them using intervals on a number line.
Examples:
- U6 L5: If the table has the following values: (1, 3) and (4, 9), the slope would be (9-3)/(4-1) = 2.
- U6 L6: If the table has the values: (0, 2), (1, 4), and (2, 6), the y-intercept would be 2.
- U6 L7: If the table shows constant differences in the y-values, such as (1, 3), (2, 5), and (3, 7), the function is linear. If the differences are not constant, such as (1, 3), (2, 4), and (3, 8), the function is nonlinear.
- U6 L7: If the graph shows a straight line, the function is linear. If it shows a curve, the function is nonlinear.
- U6 L7: If the equation has a degree of 1, such as y = 2x + 3, it is linear. If it has a degree greater than 1, such as y = x^2 + 3, it is nonlinear.
- U6 L8: In the function y = 2x + 3, the rate of change is 2 and the y-intercept is 3.
- U6 L9: For the linear function y = 2x + 3, the domain can be any real number, and the range can be any real number greater than or equal to 3. In inequality notation, the domain would be (-∞,∞) and the range would be [3,∞). In interval notation, the domain would be (-∞,∞) and the range would be [3,∞).