Instructional Video9:48
Brian McLogan

Graphing rational functions using 5 steps

12th - Higher Ed
👉 Learn how to graph a rational function. To graph a rational function, we first find the vertical and horizontal or slant asymptotes and the x and y-intercepts. After finding the asymptotes and the intercepts, we graph the values and...
Instructional Video1:58
Brian McLogan

How to find the vertical and horizontal asymptotes of a rational function

12th - Higher Ed
👉 Learn how to find the vertical/horizontal asymptotes of a function. An asymptote is a line that the graph of a function approaches but never touches. The vertical asymptote is a vertical line that the graph of a function approaches but...
Instructional Video4:48
Brian McLogan

Graph a reciprocal function and determine the limits of the vertical asymptotes

12th - Higher Ed
👉 Learn how to graph the reciprocal function. A reciprocal function is a rational function whose expression of the variable is in the denominator. A reciprocal function is of the form f(x) = a / (x + h) + k, where h is the vertical...
Instructional Video2:27
Brian McLogan

Finding the vertical and horizontal asymptotes

12th - Higher Ed
👉 Learn how to find the vertical/horizontal asymptotes of a function. An asymptote is a line that the graph of a function approaches but never touches. The vertical asymptote is a vertical line that the graph of a function approaches but...
Instructional Video3:19
Brian McLogan

Finding the horizontal and vertical asymptotes of a function

12th - Higher Ed
👉 Learn how to find the vertical/horizontal asymptotes of a function. An asymptote is a line that the graph of a function approaches but never touches. The vertical asymptote is a vertical line that the graph of a function approaches but...
Instructional Video9:33
Brian McLogan

Learning to graph a hyperbola with asymptotes

12th - Higher Ed
Learn how to graph hyperbolas. To graph a hyperbola from the equation, we first express the equation in the standard form, that is in the form: (x - h)^2 / a^2 - (y - k)^2 / b^2 = 1 for horizontal hyperbola or (y - k)^2 / a^2 - (x - h)^2...
Instructional Video9:10
Brian McLogan

Convert to a hyperbola to standard form to find foci, vertices, center and asymptotes

12th - Higher Ed
Learn how to graph hyperbolas. To graph a hyperbola from the equation, we first express the equation in the standard form, that is in the form: (x - h)^2 / a^2 - (y - k)^2 / b^2 = 1 for horizontal hyperbola or (y - k)^2 / a^2 - (x - h)^2...
Instructional Video6:38
Brian McLogan

How to find the asymptotes of the tangent function

12th - Higher Ed
👉 Learn how to graph a tangent function. To graph a tangent function, we first determine the period (the distance/time for a complete oscillation), the phase shift (the horizontal shift from the parent function), the vertical shift (the...
Instructional Video6:20
Brian McLogan

Graphing the Secant Function by Using Cosine

12th - Higher Ed
👉 Learn how to graph a cosecant function. To graph a cosecant function, we start with the sine graph by first determining the amplitude (the maximum point on the graph), the period (the distance/time for a complete oscillation), the...
Instructional Video5:02
Brian McLogan

Identify the Transformations and Asymptotes of Tangent Graph

12th - Higher Ed
👉 Learn how to graph a tangent function. To graph a tangent function, we first determine the period (the distance/time for a complete oscillation), the phase shift (the horizontal shift from the parent function), the vertical shift (the...
Instructional Video4:08
Brian McLogan

What is the Domain Range and Vertical Asymptote of Secant

12th - Higher Ed
👉 Learn the basics of graphing the secant and the cosecant graphs. Recall that the secant is the reciprocal of the cosine while the cosecant is the reciprocal of the sine. Also recall that the cosine graph is a sinusoidal graph with...
Instructional Video19:06
Brian McLogan

Master determining the center,vertices, foci and aymptotes of a hyperbola center not at origin

12th - Higher Ed
Master determining the center,vertices, foci and aymptotes of a hyperbola center not at origin
Instructional Video16:59
Brian McLogan

Master Graphing rational functions Part 2 using symmetry

12th - Higher Ed
Master Graphing rational functions Part 2 using symmetry
Instructional Video13:12
Brian McLogan

Master Determining the vertices, foci, and aymptotes of a hyperbola by completing the square

12th - Higher Ed
Master Determining the vertices, foci, and aymptotes of a hyperbola by completing the square
Instructional Video5:44
Brian McLogan

4f Characteristics of Cotangent (Parts of the Cotangent Graph)

12th - Higher Ed
4f Characteristics of Cotangent (Parts of the Cotangent Graph)
Instructional Video11:05
Brian McLogan

Graphing the Cotangent Function

12th - Higher Ed
👉 Learn how to graph a cotangent function. To graph a cotangent function, we first determine the period (the distance/time for a complete oscillation), the phase shift (the horizontal shift from the parent function), the vertical shift...
Instructional Video5:20
Brian McLogan

How to identify the parts of a hyperbola when the center is not at the origin

12th - Higher Ed
Learn how to graph hyperbolas. To graph a hyperbola from the equation, we first express the equation in the standard form, that is in the form: (x - h)^2 / a^2 - (y - k)^2 / b^2 = 1 for horizontal hyperbola or (y - k)^2 / a^2 - (x - h)^2...
Instructional Video7:01
Brian McLogan

Complete the square then graph and identify parts of an hyperbola

12th - Higher Ed
Learn how to graph hyperbolas. To graph a hyperbola from the equation, we first express the equation in the standard form, that is in the form: (x - h)^2 / a^2 - (y - k)^2 / b^2 = 1 for horizontal hyperbola or (y - k)^2 / a^2 - (x - h)^2...
Instructional Video12:33
Brian McLogan

Learn How to Graph the Secant Function with a Change in Period

12th - Higher Ed
👉 Learn how to graph a secant function. To graph a secant function, we start with the cosine graph by first determining the amplitude (the maximum point on the graph), the period (the distance/time for a complete oscillation), the phase...
Instructional Video9:04
Brian McLogan

Graph the secant function with a phase shift

12th - Higher Ed
👉 Learn how to graph a secant function. To graph a secant function, we start with the cosine graph by first determining the amplitude (the maximum point on the graph), the period (the distance/time for a complete oscillation), the phase...
Instructional Video3:10
Brian McLogan

Transformations of the tangent function

12th - Higher Ed
👉 Learn how to graph a tangent function. To graph a tangent function, we first determine the period (the distance/time for a complete oscillation), the phase shift (the horizontal shift from the parent function), the vertical shift (the...
Instructional Video7:24
Brian McLogan

Graphing Cotangent with a Phase Shift and Vertical Translation

12th - Higher Ed
👉 Learn how to graph a cotangent function. To graph a cotangent function, we first determine the period (the distance/time for a complete oscillation), the phase shift (the horizontal shift from the parent function), the vertical shift...
Instructional Video11:05
Brian McLogan

How to graph a rational function using 6 steps

12th - Higher Ed
👉 Learn how to graph a rational function. To graph a rational function, we first find the vertical and horizontal or slant asymptotes and the x and y-intercepts. After finding the asymptotes and the intercepts, we graph the values and...
Instructional Video5:20
Brian McLogan

How does the reciprocal function relate to the other basic functions

12th - Higher Ed
👉 Learn all about reciprocal functions. A reciprocal function is a function of the form f(x) = 1/x. The graph of a reciprocal function is composed of the vertical and the horizontal asymptotes and the points where the curve turns. For...