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Questions and Answers
What does the discriminant of a quadratic equation indicate?
What does the discriminant of a quadratic equation indicate?
- The number of real solutions to the equation (correct)
- The slope of the function's graph
- The vertex of the quadratic function
- The maximum or minimum value of the function
How do you determine if a function is increasing or decreasing over an interval based on its graph?
How do you determine if a function is increasing or decreasing over an interval based on its graph?
- By examining the slope of the tangent line at points in the interval (correct)
- By checking the y-values only at the endpoints of the interval
- By determining the vertex of the function
- By analyzing the x-intercepts of the graph
When given two points on a graph, how can you determine the slope of the line connecting them?
When given two points on a graph, how can you determine the slope of the line connecting them?
- By subtracting the y-coordinates and dividing by the difference of the x-coordinates (correct)
- By finding the product of their x-coordinates
- By subtracting the y-coordinates and dividing by the x-coordinates
- By averaging their coordinates
What is the proper way to substitute values into a function and simplify?
What is the proper way to substitute values into a function and simplify?
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In what scenario would you use a piecewise function?
In what scenario would you use a piecewise function?
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Study Notes
Modeling Relationships
- Construct algebraic functions representing relationships between two variables. Expect six questions on this topic.
Function Evaluation
- Determine the output (y-value) of a function given its symbolic representation, a table of values, a graph, or a piecewise definition. Three questions will cover this.
Function Simplification
- Substitute values into functions and simplify using the order of operations (PEMDAS/BODMAS). One question is expected.
Absolute Value Equations and Inequalities
- Solve equations and inequalities involving absolute value. Two questions will be on absolute value equations and one on inequalities.
Linear Functions
- Write the equation of a line given a perpendicular line or two points on the line. There will be one question for each scenario.
- Calculate the slope of a line. One question expected.
- Solve linear inequalities. Expect two questions.
Descriptive Statistics
- Calculate the mean (average) and median of a data set. One question each.
Rate of Change
- Calculate the average rate of change of a function. One question expected on this topic
Function Transformations
- Identify and apply transformations (translations) to functions. One question expected
Analyzing Graphs
- Identify intervals where a function is increasing or decreasing from its graph. One question.
Quadratic Functions
- Determine the domain and range of a quadratic function. One question.
- Find the vertex of a quadratic function. Expect one question.
- Use the discriminant to determine the number of solutions (real roots) of a quadratic equation. One question.
- Solve quadratic equations (using factoring, quadratic formula, etc.). Four questions expected.
- Solve quadratic inequalities. One question.
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