Pre Calculus Mastered

Explore the coordinate plane, including the x and y axes, the origin, and quadrants, and how points are located by their x and y coordinates.

Learn to evaluate a function by substituting values into the placeholder and applying the rule to generate outputs, with notes on domain, range, and independent versus dependent variables.

Discover how to find a function's domain, including rational functions by setting the denominator to zero and excluding those values, with notes on non-rational and square-root domains.

Explore the range of a function as the set of outputs produced from inputs, contrasted with the domain, with examples like f(x)=2x+1 and f(x)=x^2 showing nonnegative outputs.

Learn how graphs represent functions as pictures by plotting input-output pairs, linking domain and range, and graphing functions such as f(x)=x+1 and f(x)=x^2.

Explore piecewise functions by defining f(x) on separate intervals with distinct formulas, including domain, range, endpoints, holes, and inclusive or exclusive bounds.

Learn to extract information from a graph by locating x and reading the corresponding y as f(x), or finding x from a given y using lines.

Learn to find a graph's domain and range by identifying the x values fed into the function and the corresponding y values, including gaps in piecewise graphs.

Explore how to add, subtract, multiply, and divide two functions, and evaluate the resulting function at given x values, illustrated with f(x)=x^2 and g(x)=x+1 and a graph example.

Discover how to find the range of a function algebraically by computing its inverse and using the inverse's domain as the original function's range, illustrated with examples.

Master polynomials by recognizing many-term structure, identifying variables, constants, and powers, and determining degree, leading coefficient, and leading term, while noting nonnegative powers and restrictions on division.

Explore local extrema, including local maximum and local minimum, on graphs and polynomials, and learn that a degree n polynomial has at most n minus one local extrema.

Apply the factor theorem by substituting c into P(x); if P(c) equals zero, x minus c is a factor. Factor polynomials using division or synthetic division with a root.

Apply the rational zeros theorem to identify possible zeros of a polynomial as p/q, where p divides the constant term and q divides the leading coefficient.

Explore slant asymptotes in rational functions where the numerator's degree exceeds the denominator's by one, and learn how the quotient determines the asymptote and how the graph approaches it.

Explore exponential functions, where f(x) = a^x with a > 0 and a ≠ 1, and where the base is a number and the exponent is a real variable.

Explore the graph of logarithmic functions with base a, inverse of exponentials, noting domain (0, infinity), range all real numbers, an asymptote at x=0, and crossing the x-axis at (1,0).

Explore the natural logarithm as the inverse of the natural exponential, using ln (log base e) and its domain rules.

Master the core logarithm laws, including product, quotient, and power rules, apply the change of base formula, and simplify logs with base 10 conventions for clear problem solving.

explore sine and cosine graphs, applying amplitude and period changes, vertical shifts, and phase shifts to graph transformations, including left and right shifts and reflections across the x-axis.

Explore secant and cosecant graphs as reciprocals of cosine and sine, learn their vertical asymptotes and period 2π, and how shifting the graphs yields one complete period.

Identify the domain and range of sine, cosine, and tangent; note tangent has vertical asymptotes, and transform ranges via inequalities, e.g., 3 sin(5x) - 2 yields [-5, 1].

Explore the domain and range of sec, csc, cot, and tangent by analyzing their graphs, vertical asymptotes, and how input and constant changes alter domain and range.

Examine the domain and range of cotangent, cosecant, and secant, focusing on vertical asymptotes and transformed forms like 5x - π + 8 and x - 2π.