x in two places 34 videos
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The Reflection y = f(-x)
Precalculus Introduction to Functions
How to reflect the graph of y = f(x) across the y-axis.
functions parent functions reflection -
Graphing the Transformation y = a f(x) + k
Precalculus Introduction to Functions
How to graph the transformation y = a f(x) + k when f(x) = abs(x).
functions transformations stretch compression reflection vertical shift turning point -
Graphing the Transformation y = f(x - h)
Precalculus Introduction to Functions
How to graph y = f(x ? h) when f(x) = sqrt(x), and what kind of transformation to expect.
functions transformations horizontal shift end point -
The Resultant of Two Forces
Precalculus Vectors and Parametric Equations
How to find the resultant of two forces when they are parallel, opposite, or perpendicular in direction.
Forces Resultant Vector Addition Magnitude Direction The Pythagorean Theorem -
Symmetry of Polar Graphs
Precalculus Polar Coordinates and Complex Numbers
How to determine if the graph of a polar equation is symmetric about the x-axis.
polar graph polar equation symmetry reflection x axis symmetric about the x axis -
Graphing Polynomial Functions with Repeated Factors
Precalculus Polynomial and Rational Functions
How we identify the behavior of a polynomial graph near an x-intercept.
polynomial functions leading term end behavior x intercepts -
Intercepts and Asymptotes of Tangent Functions
Precalculus Trigonometric Functions
How to find the x-intercepts and vertical asymptotes of the graph of y = tan(q).
sine cosine tangent zeros x intercepts vertical asymptotes -
The Reciprocal Transformation
Precalculus Polynomial and Rational Functions
How to graph the reciprocal of a linear function.
the reciprocal transformation x intercepts asymptotes -
Limits of Rational Functions
Precalculus Polynomial and Rational Functions
How to evaluate the limit of k/x^n as x goes to infinity (or negative infinity).
rational functions limits infinity -
Adding Vectors
Precalculus Vectors and Parametric Equations
How to add vectors geometrically two ways.
Displacement Vector Addition Head to Tail Method Parallelogram Method -
The Dot Product of Vectors
Precalculus Vectors and Parametric Equations
How to compute the dot product of two vectors.
vector components component form dot product scalar product -
The Angle Between Vectors
Precalculus Vectors and Parametric Equations
How to compute the angle between two vectors.
dot product angle between vectors position vectors -
Multiplying Complex Numbers
Precalculus Polar Coordinates and Complex Numbers
How to multiply two complex numbers in trigonometric form.
complex numbers trigonometric form modulus argument -
Dividing Complex Numbers
Precalculus Polar Coordinates and Complex Numbers
How to divide two complex numbers in trigonometric form.
complex numbers trigonometric form modulus argument conjugate -
The Inverse of a Square Matrix
Precalculus Systems of Linear Equations and Matrices
How to determine whether two matrices are inverses.
matrices square matrices the identity matrix matrix multiplication invertible inverse matrix -
The Cross Product of Vectors
Precalculus Systems of Linear Equations and Matrices
How to compute the cross product of two 3D vectors.
unit vectors components cross product determinant -
Limits at a Glance
Precalculus Polynomial and Rational Functions
How to quickly find the limit of a rational function as x goes to infinity.
rational functions polynomials degree limits infinity -
Cramer's Rule
Precalculus Systems of Linear Equations and Matrices
How to solve a system of two linear equations with two unknowns using Cramer's rule.
systems of linear equations Cramer's rule determinant coefficient matrix -
Area With the Cross Product
Precalculus Systems of Linear Equations and Matrices
How to show that the magnitude of the cross product of two vectors gives the area of the parallelogram determined by those two vectors.
cross product magnitude of vectors dot product angle between vectors area parallelogram -
Parallel Planes and Lines
Precalculus Equations of Lines, Parabolas and Circles
How to identify parallel lines, a line parallel to a plane, and two parallel planes.
parallel lines skew plane
