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- https://math.libretexts.org/Bookshelves/Precalculus/Corequisite_Companion_to_Precalculus_(Freidenreich)/1%3A_Simplifying_Expressions/1.03%3A_Function_Notation_and_Simplify_ExpressionsThe goal of this section is to practice function notation. Functions have many interconnected mathematical concepts. Therefore, more detail about functions will emerge in your Precalculus course. This...The goal of this section is to practice function notation. Functions have many interconnected mathematical concepts. Therefore, more detail about functions will emerge in your Precalculus course. This section will practice the correspondence of inputs to outputs using function notation, giving further practice with the properties introduced in previous sections.
- https://math.libretexts.org/Bookshelves/Precalculus/Corequisite_Companion_to_Precalculus_(Freidenreich)
- https://math.libretexts.org/Bookshelves/Precalculus/Corequisite_Companion_to_Precalculus_(Freidenreich)/zz%3A_Back_Matter/10%3A_Index
- https://math.libretexts.org/Bookshelves/Precalculus/Corequisite_Companion_to_Precalculus_(Freidenreich)/6%3A_Radical_ExpressionsLearning Objectives Evaluate \(n^{\text{th}}\)-root radicals. Simplify radicals by applying appropriate properties. Distinguish between like radicals and unlike radicals. Add and subtract like radical...Learning Objectives Evaluate \(n^{\text{th}}\)-root radicals. Simplify radicals by applying appropriate properties. Distinguish between like radicals and unlike radicals. Add and subtract like radicals. Multiply and divide radicals, simplifying results.
- https://math.libretexts.org/Bookshelves/Precalculus/Corequisite_Companion_to_Precalculus_(Freidenreich)/4%3A_Inequalities/4.04%3A_Absolute_Value_Equations_and_Inequalities_as_Applied_to_DistanceThe absolute value function, denoted y = |x|, takes any negative real number input and outputs the positive version of that number. Nonnegative numbers are left unchanged. Measuring distance is a goo...The absolute value function, denoted y = |x|, takes any negative real number input and outputs the positive version of that number. Nonnegative numbers are left unchanged. Measuring distance is a good application to demonstrate the usefulness of this function. Distance is never negative.
- https://math.libretexts.org/Bookshelves/Precalculus/Corequisite_Companion_to_Precalculus_(Freidenreich)/3%3A_GraphsLearning Objectives Interpret, from function notation, an action or several actions to be taken on a known function, \(f\), in order to sketch the transformed function. Sketch transformations from \(9...Learning Objectives Interpret, from function notation, an action or several actions to be taken on a known function, \(f\), in order to sketch the transformed function. Sketch transformations from \(9\) familiar functions. Write the equation of a function associated with descriptive transformations such as shifting left, right, up, or down, reflecting, stretching, and compressing of its parent function.
- https://math.libretexts.org/Bookshelves/Precalculus/Corequisite_Companion_to_Precalculus_(Freidenreich)/3%3A_Graphs/3.02%3A_Transformations_of_Common_GraphsThe transformation of graphs, using common functions, will be a skill that will bring insight to graphing functions quickly and painlessly. Anticipating how a graph of a function will look, and transf...The transformation of graphs, using common functions, will be a skill that will bring insight to graphing functions quickly and painlessly. Anticipating how a graph of a function will look, and transforming old graphs to new graphs, is a skill we will explore in this section. Mastering this skill will give you a leg up on understanding analytic geometry, a key component to calculus.
- https://math.libretexts.org/Bookshelves/Precalculus/Corequisite_Companion_to_Precalculus_(Freidenreich)/8%3A_Problem_Solving/8.01%3A_Arithmetic_SequencesWe can describe a sequence in words (e.g. a sequence of even numbers.) but can we describe the sequence mathematically? That is, can we describe the pattern of the sequence of even numbers using a for...We can describe a sequence in words (e.g. a sequence of even numbers.) but can we describe the sequence mathematically? That is, can we describe the pattern of the sequence of even numbers using a formula? Absolutely! This section will explore arithmetic sequences, how to identify them, mathematically describe their terms, and the relationship between arithmetic sequences and linear functions. Let’s get started!
- https://math.libretexts.org/Bookshelves/Precalculus/Corequisite_Companion_to_Precalculus_(Freidenreich)/2%3A_Polynomials/2.03%3A_Review_of_FactoringFactoring is a necessary skill to have in precalculus and all math classes beyond precalculus. Factoring is a tool to simplify expressions and eases calculations. It helps us identify the roots of pol...Factoring is a necessary skill to have in precalculus and all math classes beyond precalculus. Factoring is a tool to simplify expressions and eases calculations. It helps us identify the roots of polynomials, making quick work of graphing without any need for computers or graphing calculators. In the same way arithmetic rules inform algebraic properties, prime factorization of real numbers informs polynomials factorization.
- https://math.libretexts.org/Bookshelves/Precalculus/Corequisite_Companion_to_Precalculus_(Freidenreich)/5%3A_Rational_Expression/5.01%3A_Simplify_Rational_ExpressionsRational numbers are sometimes informally called fractions. Numbers such as 3/4 and −1/5 are rational numbers. When simplifying rational expressions, look for groups of variables or numbers that c...Rational numbers are sometimes informally called fractions. Numbers such as 3/4 and −1/5 are rational numbers. When simplifying rational expressions, look for groups of variables or numbers that can be canceled to one. Cancel as many times as permits within a rational expression.
- https://math.libretexts.org/Bookshelves/Precalculus/Corequisite_Companion_to_Precalculus_(Freidenreich)/4%3A_Inequalities/4.02%3A_Interval_NotationInequalities slice and dice the real number line into segments of interest or intervals. An interval is a continuous, uninterrupted subset of real numbers. How can we notate intervals with simplicity?...Inequalities slice and dice the real number line into segments of interest or intervals. An interval is a continuous, uninterrupted subset of real numbers. How can we notate intervals with simplicity? The table below introduces Interval Notation.
