Graph Functions Using Intercepts Videos - Free Educational Videos for Students in K - 12

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Using the x- and y- Intercepts to Graph a Linear Function


By PatrickJMT

This video shows us how to use two important features of a linear function, the x- and y- intercepts, to graph the function. Remember that we only need two points to determine a line, and often, the intercepts are extremely easy to find.

Using the x- and y- Intercepts to Graph a Linear Function


By PatrickJMT

This video shows us how to use two important features of a linear function the x- and y- intercepts to graph the function. Remember that we only need two points to determine a line and often the intercepts are extremely easy to find.

Inverse Functions | MathHelp.com


By MathHelp.com

In this example, we’re given a relation in the form of a chart, and we’re asked to find the inverse of the relation, then graph the relation and its inverse. To find the inverse of a relation, we simply switch the x and y values in each point. In other words, the point (1, -4) becomes (-4, 1), the point (2, 0) becomes (0, 2), the point (3, 1) becomes (1, 3), and the point (6, -1) becomes (-1, 6). Next, we’re asked to graph the relation and its inverse, so let’s first graph the relation. Notice that the relation contains the points (1, -4,), (2, 0), (3, 1), and (6, -1). And the inverse of the relation contains the points (-4, 1), (0, 2), (1, 3), and (-1, 6). Finally, it’s important to understand the following relationship between the graph of a relation and its inverse. If we draw a diagonal line through the coordinate system, which is the line that has the equation y = x, notice that the relation and its inverse are mirror images of each other in this line. In other words, the inverse of a relation is the reflection of the original relation in the line y = x.

Systems of Three Equations | MathHelp.com


By MathHelp.com

Here we’re asked to graph the following function and use the horizontal line test to determine if it has an inverse. And if so, find the inverse function and graph it. So let’s start by graphing the given function, f(x) = 2x – 4, and remember that f(x) is the same as y, so we can rewrite the function as y = 2x – 4. Now, we simply graph the line y = 2x – 4, which has a y-intercept of -4, and a slope of 2, or 2/1, so we go up 2 and over 1, plot a second point and graph our line, which we’ll call f(x). Next, we’re asked to use the horizontal line test to determine if the function has an inverse. Since there’s no way to draw a horizontal line that intersects more than one point on the function, the function does have an inverse. So we need to find the inverse and graph it. To find the inverse, we switch the x and the y in original function, y = 2x – 4, to get x = 2y – 4. Next, we solve for y, so we add 4 to both sides to get x + 4 = 2y, and divide both sides by 2 to get 1/2x + 2 = y. Next, let’s flip our equation so that y is on the left side, and we have y = 1/2x + 2. Finally, we replace y with the notation that we use for the inverse function of f, as shown here. And remember that we’re asked to graph the inverse as well, so we graph y = ½ x + 2. Our y-intercept is positive 2, and our slope is ½, so we go up one and over 2, plot a second point, graph the line, and label it as the inverse function of f. Notice that the graph of the inverse function is a reflection of the original function in the line y = x.

Qtr 2, Lesson 5: Graphing Linear Equations in Slope-Intercept Form


By Stan Lisle

This lesson teaches about Slope - Intercept Form, and how to use this form to graph equations, or to determine the equation of lines. The video contains questions after each section to help guide the student through the lessons.

12 - What are Inverse Functions? (Part 1) - Find the Inverse of a Function & Graph


By Math and Science

Quality Math And Science Videos that feature step-by-step example problems!

Example Problem - Linear Functions (Slope)


By Khan Academy

This video lecture series on Worked Examples in Algebra from Khan Academy includes Solving Equations Solving Word Problems Solving for a variable Absolute Value and Number Lines Patterns in Sequences Functional Relationships Domain and Range Rate Problems Linear Functions Slope of a Line X and Y intercepts Equation of a Line Parallel Lines Perpendicular Lines Solving Inequalities and more...

Area Between Two Curves


By The Organic Chemistry Tutor

This calculus video tutorial provides a basic introduction in finding the area between two curves with respect to y and with respect to x. It explains how to set up the definite integral to calculate the area of the shaded region bounded by the two curves. In order to find the points of intersection, you need to set the two curves equal to each other and solve for x or y. You need to be familiar with some basic integration techniques for this lesson. This video contains plenty of examples and practice problems.

16 - Domain and Range of a Quadratic Function - Part 1 (Graphing Quadratics)


By Math and Science

Quality Math And Science Videos that feature step-by-step example problems!

More examples of constructing linear equations in slope-intercept form | Algebra I | Khan Academy


By Khan Academy

Watch this video to learn how to derive and graph a linear equation from either: two points on the line the y-intercept and the slope A linear equation (in slope intercept form) is a line of the form y = mx + b where m is the slope and b is the y-intercept--the value at which the line intersects the y-axis.

More examples of constructing linear equations in slope-intercept form | Algebra I | Khan Academy


By Khan Academy

Watch this video to learn how to derive and graph a linear equation from either: two points on the line the y-intercept and the slope A linear equation (in slope intercept form) is a line of the form y = mx + b where m is the slope and b is the y-intercept--the value at which the line intersects the y-axis.

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12 - Writing Quadratic Functions in Vertex Form - Part 1 (Graphing Parabolas)


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05 - Quadratic Systems of Equations (With Lines, Circles, Ellipses, Parabolas & Hyperbolas)


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