determine the domain and range of a linear function in mathematical problems; determine reasonable domain and range values for real-world situations, both continuous and discrete; and represent domain and range using inequalities
write linear equations in two variables in various forms, including y = mx + b, Ax + By = C, and y - y1 = m (x - x1), given one point and the slope and given two points
determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms, including y = mx + b, Ax + By = C, and y - y1 = m (x - x1 )
calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world problems
graph linear functions on the coordinate plane and identify key features, including x- intercept, y- intercept, zeros, and slope, in mathematical and real-world problems
determine the effects on the graph of the parent function f(x) = x when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d
calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association
write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems
solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides
solve linear inequalities in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides
write equations of quadratic functions given the vertex and another point on the graph, write the equation in vertex form (f(x) = a(x - h)2 + k), and rewrite the equation from vertex form to standard form (f(x) = ax2 + bx + c)
graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x- intercept, y- intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry
determine the effects on the graph of the parent function f(x) = x2 when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d
write exponential functions in the form f(x) = abx (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay
graph exponential functions that model growth and decay and identify key features, including y- intercept and asymptote, in mathematical and real-world problems
determine the quotient of a polynomial of degree one and polynomial of degree two when divided by a polynomial of degree one and polynomial of degree two when the degree of the divisor does not exceed the degree of the dividend
decide if a binomial can be written as the difference of two squares and, if possible, use the structure of a difference of two squares to rewrite the binomial
