Learning Objectives
Learning Objectives
- Understand one-variable and two-variable data and describe the differences among the types of functions.
- Visualize and graphically represent one-variable and two-variable data.
- Understand the concept of a function as a representation.
- Use set builder notation and interval notation to describe the domain and range of a function.
- Interpret the domain and the range of a representation as mathematical objects and in a context of an application.
- Distinguish between linear and non-linear functions.
- Evaluate the average rate of change of a function, using the notion of the difference quotient.
- Fluently perform algebraic computations related to linear and quadratic expressions.
- Solve linear equations and absolute value equations algebraically, numerically, and graphically.
- Write linear functions and understand the relationship between parallel and perpendicular lines.
- Solve linear inequalities (including compound inequalities) and absolute value inequalities algebracically, numerically, and graphically.
- Solve quadratic equations using factoring, the square root property, completing the square, or through the quadratic formula.
- Understand the effect of the discriminant on the nature of roots or solutions to a quadratic equation.
- Understand the basic concepts of complex numbers and their arithmetic operations.
- Solve quadratic inequalities graphically and numerically.
- Perform transformations of graphs, which include horizontal and vertical shifts, stretching and shrinking, reflection of graphs, and a combination of multiple transformations.
- Construct linear and quadratic models to fit data and use them to explain and to analyze real life scenarios.
- Analyze the behavior of functions (might also include other types of functions), increasing and decreasing, while using the concepts of average rate of change and the difference quotient.
- Use linear functions and linear piece-wise functions to model data of examples such as CO2 emissions, ice deposits, birth rate, temperature, sales, cost, and college tuition.
- Understand the difference between interpolation and extrapolation.
- Obtain Linear Regression models after generating scatter plots of data, with the use of technology (Calculator, Geogebra, Desmos, or other software).
- Modeling with quadratic functions.
- Analyzing the behavior of the model graphically or through the vertex and its significance.
- Use quadratic regression to describe data that has a parabolic shape.
