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Questions and Answers
What is the definition of Domain?
What is the definition of Domain?
- Set of all OUTPUT or Y-INTERCEPTS values
- Rate of change
- Set of all INPUT or X-INTERCEPTS values (correct)
- Parent function for linear functions
What is the definition of Range?
What is the definition of Range?
- Parent function for linear functions
- Rate of change
- Set of all INPUT or X-INTERCEPTS values
- Set of all OUTPUT or Y-INTERCEPTS values (correct)
The equation Y=X² represents the parent function for linear functions.
The equation Y=X² represents the parent function for linear functions.
False (B)
Changing the SLOPE of a line affects the ______.
Changing the SLOPE of a line affects the ______.
Changing the Y-INTERCEPT of a line causes a ______ shift.
Changing the Y-INTERCEPT of a line causes a ______ shift.
If a line decreases from left to right, then the slope is?
If a line decreases from left to right, then the slope is?
If a line increases from left to right, then the slope is?
If a line increases from left to right, then the slope is?
What is another term for 'rate of change'?
What is another term for 'rate of change'?
If something was labeled meters per second, what does it represent?
If something was labeled meters per second, what does it represent?
Lines with the same slope are called parallel.
Lines with the same slope are called parallel.
Scatterplots that have data going 'downhill' direction have positive correlation.
Scatterplots that have data going 'downhill' direction have positive correlation.
Scatterplots that have data all over the place have no correlation.
Scatterplots that have data all over the place have no correlation.
Zeros, roots, and solutions all mean what?
Zeros, roots, and solutions all mean what?
When solving quadratic equations, we set the equations to _____ before solving.
When solving quadratic equations, we set the equations to _____ before solving.
What is the highest/lowest point on a parabola called?
What is the highest/lowest point on a parabola called?
What shape is the graph of a linear function?
What shape is the graph of a linear function?
What shape is the graph of a quadratic function?
What shape is the graph of a quadratic function?
When the boundary line is dashed and graphed, are points on the boundary line considered a solution?
When the boundary line is dashed and graphed, are points on the boundary line considered a solution?
When a system of equations is graphed, the solution is where the lines do what?
When a system of equations is graphed, the solution is where the lines do what?
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Study Notes
Algebra Concepts
- Domain: The set of all possible input values (X-values) for a function.
- Range: The set of all possible output values (Y-values) for a function.
Functions
- Y=X²: The parent function for quadratic functions, demonstrating parabolic behavior.
- Steepness: A line's slope determines its steepness; changing the slope affects how steep the line appears.
- Vertical Shift: Modifying the Y-intercept of a line results in a vertical shift up or down.
Slope Characteristics
- Negative Slope: A line that decreases from left to right indicates a negative slope.
- Positive Slope: A line that increases from left to right indicates a positive slope.
- Slope Definition: Frequently described as the "rate of change," representing the rise over run in a graph.
Correlation Types
- Positive Correlation: Scatterplots that trend upwards, indicating that as one variable increases, so does the other.
- Negative Correlation: Scatterplots that trend downwards, indicating that as one variable increases, the other decreases.
- No Correlation: Scatterplots with no discernible pattern show data points scattered randomly.
Equation Solutions
- X-Intercepts: Also referred to as zeros, roots, or solutions, these are the points where a function crosses the X-axis.
- Quadratic Equations: To solve quadratic equations, set the equation equal to zero (0) before proceeding.
- Vertex: The highest or lowest point on a parabola, crucial for understanding the function's maximum or minimum behavior.
Graphing Characteristics
- Line: The graphical representation of a linear function results in a straight line.
- U-Shaped (Parabola): Quadratic functions are represented graphically as a U-shaped curve.
- Boundary Line: In inequality graphs, if the boundary line is dashed, then points on the boundary are not included in the solution set.
Systems of Equations
- Intersection: The solution to a system of equations is found at the point where the lines intersect on a graph.
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