Related Issues (20)
- Create equations and inequalities in one variable and use them to solve problems.Tasks are limited to linear, quadratic, or exponential equations with integer exponents HOT 1
- Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs. Tasks are limited to constructing linear and exponential functions in simple context (not multi-step).
- Determine an explicit expression, a recursive process, or steps for calculation from a context. HOT 1
- Recognize that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. HOT 1
- Recognize situations in which one quantity changes at a constant rate per unit interval relative to another HOT 1
- Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs. HOT 1
- Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
- Graph linear and quadratic functions and show intercepts, maxima, and minima.
- For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries and end behavior. HOT 1
- Interpret the parameters in a linear or exponential function in terms of a context. For example, the total cost of an electrician who charges 35 dollars for a house call and 50 dollars per hour would be expressed as the function y = 50x + 35. If the rate were raised to 65 dollars per hour, describe how the function would change. Exponential functions are limited to those with domains in the integers.
- Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Tasks are limited to linear, quadratic, piecewise-defined (including step and absolute value functions), and exponential functions with domains in the integers.
- Recognize that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
- Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. HOT 1
- Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a table, a description of a relationship, or two input-output pairs. HOT 1
- Graph linear and quadratic functions and show intercepts, maxima, and minima. HOT 2
- Create equations in two or more variables to represent relationships between quantities; graph equations with two variables on coordinate axes with labels and scales.
- Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. HOT 1
- Interpret the parameters in a linear or exponential function in terms of a context. For example, the total cost of an electrician who charges 35 dollars for a house call and 50 dollars per hour would be expressed as the function y = 50x + 35. If the rate were raised to 65 dollars per hour, describe how the function would change. HOT 1
- Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions.) HOT 1
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