Linear Functions and Beyond
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Represent real-world problems using a system of linear equations and/or inequalities in two or three variables. Solve such systems graphically or with matrices, as appropriate to the system, with technology. Interpret the solution and determine whether it is reasonable.
Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, k f(x), f(kx), or f(x + k). Identify and analyze transformations within a real-world context.
Recognize functional relationships in real-world contexts. Translate fluently among multiple representations (graphs, tables, equations, and verbal descriptions).
Model real-world situations involving arithmetic sequences and understand that they can be defined both recursively and with an explicit formula.
Solve a system of equations and/or inequalities consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with technology (e.g., find the points of intersection between the line y = –3x and the parabola y = x² − 6x − 5).