Algebra 2 Precalculus and Trigonometry (LEVEL: 11 or 12 gd)

Define a function as a mapping from each input to a unique output, using ordered pairs; relation is a set of pairs with domain as inputs and range as outputs.

Explore how domain and range define a function, using input-output mappings and blob notation, with examples like g(1)=8 and g(2)=6 to illustrate function notation.

Analyze the difference between relations and functions, identify inputs and outputs, and practice reading function notation and solving f(x)=1 from the given tables.

Read pages 14-20 (pdf 24-30) and practice evaluating functions by substitution into f(x) and g(x); apply the foil method and distributive property to expand x^2+2xh+h^2.

Explore evaluating functions by substituting values into g(m) = sqrt(m - 4), solving g(m) = 2, and deriving y as a function of x from x - 8y^3 = 0.

Using figure seven to solve F of x equals one, locate where the graph has y equals one on figure nine; solutions are x equals zero and x equals two.

Practice substituting values into function notation, evaluate f(-3) and f(2), then analyze f(-a) and a minus f(a), and expand f(a+h) for f(x) = -5x^2 + 2x - 1 with negatives.

the lecture demonstrates multiplying a plus h by itself using the distributive property and foiling (first, outer, inner, last), yielding a^2 plus two ah plus h^2, and notes commutativity.

Practice simplifying a rational expression by factoring and canceling common factors, revealing x plus a plus 2. Then evaluate k(2) and solve k(t)=7 to find t=4.

Explore function notation, inputs, and outputs; identify when a relation is a function; and demonstrate evaluating functions, foiling, factoring, and the zero product property.

Explore function basics by determining whether y is a function of x and evaluating f at specified inputs, while reviewing exponents and real-world notation in a GMP population problem.

Explore evaluating piecewise and standard functions, applying exponent rules and square roots, and interpreting a real-world function linking population to garbage generation through problems 29, 35, 53, 73, and 88.

Assigns day four problems 21, 24, 32, 36, 40, 41, 54, 55, 56, 57. Explores function concepts, the derivative via the limit, and the vertical and horizontal line tests.

Explore functions with vertical line test and not a function cases, factor and apply zero product property, and preview calculus with a derivative expression, plus one-to-one and horizontal line tests.

Master the toolkit functions—constant, identity, absolute value, x squared, x cubed, reciprocal, reciprocal squared, square root, and cube root—and their graphs, domains, and use in building other functions.

Read pages 25–28 and pdf pages 35–38, work problems 37–39 and 89 to evaluate functions, solve quadratics, and relate cubic yards of dirt to garden area in square feet.

Master evaluating functions and solving equations using factoring, the zero-product property, and square roots through examples like f(5), f(7), and f(x)=4.

Learn to determine the domain of functions, including division by zero limitations and square root versus cube root cases, with problems 1–8 and 13–15.

Identify the domain of functions by examining valid inputs, including why square roots exclude negatives and cube roots do not, and express results with interval notation using brackets and parentheses.

Advance through unit six by reading pages 38–44 and solving problems 9,10,11,16,27,28,29,57,58,59, using hints to practice domain and range, the square root, and interval notation through repetition.

Practice solving domain and range from graphs, sketching piecewise and asymptote graphs, evaluating piecewise functions, and translating domain into interval notation, with a real-world projectile height example.

Explore average rate of change and slope by analyzing how y changes with x, using the interval formula, and practice problems 1,5,6,7,16,17,28–32 from the assigned pages.