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Pre Algebra 23 - Scientific Notation - v.2
Scientific notation allows us to more easily express very large or very small numbers encountered in engineering and science. Using exponents, we can convert standard decimal numbers into scientific notation and vice versa.
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Algebra 94 - Rational Functions with Oblique or Curvilinear Asymptotes
In the previous lecture we saw that although a rational function may have any number of vertical asymptotes or no vertical asymptotes, rational functions will always have exactly one non-vertical asymptote. Unlike vertical asymptotes, a...
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Algebra 93 - Rational Functions and Nonvertical Asymptotes
Although a rational function may have any number of vertical asymptotes or no vertical asymptotes, rational functions will always have exactly one non-vertical asymptote. Since a function's value is undefined at a vertical asymptote, its...
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Algebra 92 - Rational Functions and Holes
In the previous lecture, we saw examples of x values that cause a rational function's numerator to be zero, where those x values produce x-axis intercepts in the function's graph. We also saw x values that cause denominator zeros that...
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Algebra 91 - Rational Functions and Vertical Asymptotes
A rational function is any function that can be written as a fraction whose numerator and denominator are polynomials. Rational functions include a broad range of possibilities. For example, since a polynomial can be a constant, a...
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Algebra 90 - Dividing Polynomials
This lecture explains a procedure used to divide polynomials that is analogous to the procedure used to divide integers called "long division". Dividing one polynomial (the dividend) by another (the divisor) produces a quotient that may...
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Algebra 89 - Multiplying Polynomial Functions
In the previous lecture we saw how polynomial functions could be added or subtracted, producing new polynomial functions with different characteristics. In this lecture we will see how to multiply polynomial functions and show how the...
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Algebra 88 - Adding and Subtracting Polynomial Functions
Adding polynomial functions produces another polynomial function. The values of this function are the sum of the values of the polynomials that were added for every possible value of the input variable(s). Fortunately, adding polynomial...
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Algebra 87 - Graphing Polynomial Functions - Part 2
When sketching the graph of a polynomial function, it may not be necessary to calculate numerous points on the graph. Many clues as to the general shape of the graph can be derived if we understand the characteristics that the graphs of...
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Algebra 86 - Graphing Polynomial Functions - Part 1
Calculators and graphing utilities are available that are capable of creating accurate graphs of polynomial functions. However, it is often desirable to sketch a quick representation of a function's graph to get a general idea of its...
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Algebra 84 - Monomial Building Blocks of Polynomial Functions
A polynomial is a sum of one or more terms called monomials. If we think of each monomial as a separate function, then a polynomial function can be thought of as a sum of these monomial functions. In previous lectures we have studied...
Curated Video
How to Subtract Using a Number Line
In this video, a teacher demonstrates how to subtract using a number line and helps students identify which number line represents a given expression. The teacher breaks down the steps and eliminates incorrect answer choices, making the...
Curated Video
Finding Unit Rate Using a Conversion Ratio
In this video, the teacher explains how to find the unit rate cost per ounce of buying a watermelon using conversion ratios. The video walks through the steps of converting from pounds to ounces and shows how to avoid common mistakes...