Instructional Video5:05
Brian McLogan

Graph the parent graph then transform it based on the function, y = -2^(x-3)

12th - Higher Ed
👉 Learn how to graph exponential functions involving horizontal shift. An exponential function is a function that increases rapidly as the value of x increases. To graph an exponential function, it is usually very useful to make the...
Instructional Video4:35
Brian McLogan

Finding and graphing the vertical and horizontal asymptotes

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 Video13:42
Brian McLogan

Learn to graph the reciprocal function using a table

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...
Instructional Video9:29
Brian McLogan

Learn how to graph a 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 Video6:16
Brian McLogan

Identify the center, foci, vertices and asymptotes then sketch graph of hyperbola

12th - Higher Ed
Identify the center, foci, vertices and asymptotes then sketch graph of hyperbola
Instructional Video5:50
Brian McLogan

Step by step graph and identify the foci, center, and vertices of 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 Video3:57
Brian McLogan

Graphing the Tangent Function with a Phase Shift

12th - Higher Ed
👉 Learn all about graphing trigonometric functions. In this playlist, we will explore how to graph the sine, cosine, tangent, cotangent, cosecant and secant function. We will explore the characteristics of each graph as well as how to...
Instructional Video8:49
Brian McLogan

Graphing the reciprocal identity with a removable discontinuity

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 Video10:50
Brian McLogan

Graph a rational function with vertical and oblique asymptotes

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 Video1:32
Brian McLogan

How to find the vertical 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 Video4:24
Brian McLogan

Finding the asymptotes and intercepts of a rational function

12th - Higher Ed
👉 Learn how to find the x and y-intercepts of a rational function. The x-intercept(s) of a function occurs when y = 0 and the y-intercept(s) of a function occurs when x = 0. To find the y-intercept of a function, we plug in zero for x...
Instructional Video3:54
Brian McLogan

Find 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 Video2:14
Brian McLogan

Find all the asymtotes and intercepts 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 Video4:57
Brian McLogan

What are the restrictions on our solutions for a rational equation

12th - Higher Ed
👉 Learn how to solve rational equations. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. There are many ways to solve rational expressions, one...
Instructional Video1:14
Brian McLogan

When a rational function has no vertical 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 Video5:13
Brian McLogan

Determining the 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 Video2:08
Brian McLogan

Identify any horizontal or vertical 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 Video2:16
Brian McLogan

Identify any Horizontal or Vertical 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 Video3:28
Brian McLogan

Learn How to Find the Domain of the Composition of Two Functions

12th - Higher Ed
Learn how to compose two functions where one or both of those functions is/are radical. To compose two functions means to express one of the functions as a function of the other function. This is done by replacing the input variable of...
Instructional Video4:44
Brian McLogan

Learn how to graph a rational function without any symmetry

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 Video14:03
Brian McLogan

Sketch the cosecant graph from scratch

12th - Higher Ed
Sketch the cosecant graph from scratch
Instructional Video7:22
Brian McLogan

learn to graph a hyperbola given the equation

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 Video6:19
Brian McLogan

How to graph secant and label the parts

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 Video2:18
Brian McLogan

Understand how to find the important characteristics of cotangent

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...