x 14 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 -
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 -
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 -
More Transformations of Sine and Cosine
Precalculus Trigonometric Functions
How the value of h affects the shape of the graph y = A sin(B(x-h)).
transformations sine period amplitude phase shift horizontal shift -
The Ellipse
Precalculus Conic Sections
All about ellipses.
ellipse co vertices vertices major axis minor axis focus foci x radius y radius -
Find an Equation of the Polynomial Function
Precalculus Polynomial and Rational Functions
How we identify the equation of a polynomial function when we are given the intercepts of its graph.
polynomial functions cubic functions x intercepts factors end behavior leading coefficient stretch factor -
Families of Polar Curves: Roses
Precalculus Polar Coordinates and Complex Numbers
How to describe Roses, the family of curves with equations r=acos(b*theta) or r=asin(b*theta) when b >=2 and is an integer.
polar graph polar equation polar curve roses symmetric about the x axis symmetric about the y axis. -
Families of Polar Curves: Conic Sections
Precalculus Polar Coordinates and Complex Numbers
How to describe the polar equations of conic sections.
polar graph polar equation polar curve conic sections focus origin pole parabola symmetric about the x axis parabola vertex
