5A determine the effects on the key attributes on the graphs of f(x) = b to the x power and f(x) = logb (x) where b is 2, 10, and e when f(x) is replaced by af(x), f(x) + d, and f(x – c) for specific positive and negative real values of a, c, and d
5B formulate exponential and logarithmic equations that model real-world situations, including exponential relationships written in recursive notation
5C rewrite exponential equations as their corresponding logarithmic equations and logarithmic equations as their corresponding exponential equations
5D solve exponential equations of the form y = ab to the x power where a is a nonzero real number and b is greater than zero and not equal to one and single logarithmic equations having real solutions
5E determine the reasonableness of a solution to a logarithmic equation
4A write the quadratic function given three specified points in the plane
4B write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening
4C determine the effect on the graph of f(x) = √x when f(x) is replaced by af(x), f(x) + d, f(bx), and f(x – c) for specific positive and negative values of a, b, c, and d
4D transform a quadratic function f(x) = ax² + bx + c to the form f(x) = a(x – h)² + k to identify the different attributes of f(x)
4E formulate quadratic and square root equations using technology given a table of data
4F solve quadratic and square root equations
4G identify extraneous solutions of square root equations
3A formulate systems of equations, including systems consisting of three linear equations in three variables and systems consisting of two equations, the first linear and the second quadratic
3B solve systems of three linear equations in three variables by using Gaussian elimination, technology with matrices, and substitution
3C solve, algebraically, systems of two equations in two variables consisting of a linear equation and a quadratic equation
3D determine the reasonableness of solutions to systems of a linear equation and a quadratic equation in two variables
3E formulate systems of at least two linear inequalities in two variables
3F solve systems of two or more linear inequalities in two variables
3G determine possible solutions in the solution set of systems of two or more linear inequalities in two variables.
2A The student applies mathematical processes to understand that functions have distinct key attributes and understand the relationship between a function and its inverse.
2B graph and write the inverse of a function using notation such as f-¹ (x);
2C describe and analyze the relationship between a function and its inverse (quadratic and square root, logarithmic and exponential), including the restriction(s) on domain, which will restrict its range
2D use the composition of two functions, including the necessary restrictions on the domain, to determine if the functions are inverses of each other.
Add and subtract polynomials of degree one and degree two.
A.10B
Multiply polynomials of degree one and degree two.
A.10C
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.
A.10D
Rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property.
A.10E
Factor if possible trinomials with real factors in the form ax^2 + bx + c including perfect square trinomials of degree two.
A.10F
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.
Determine the domain and range of exponential functions of the form f(x) =ab^x and represent the domain and range using inequalities.
A.9B
Interpret the meaning of the values of a and b in exponential functions of the form f(x) = ab^x in real-world problems.
A.9C
Write exponential functions in the form f(x) = ab^ x (where b is a rational number) to describe problems arising from mathematical and real-world situations including growth and decay.
A.9D
Graph exponential functions that model growth and decay and identify key features including y-intercept and asymptote in mathematical and real-world problems.
A.9E
Write, using technology, exponential functions that provide a reasonable fit to data and make predictions for real-world problems.
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.
A.7B
Describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions.
A.7C
Determine the effects on the graph of the parent function f(x) =x^2 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.
