The y-intercept of a function is the point at which the graph of the function crosses the y-axis. Although a function can have many x-intercepts, a function can only have one y-intercept. This is because a function must pass the vertical line test in order for it to be a function; if a vertical line intersects the graph of a relation at more than one point, it is not a function. Example The relation in the following figure is a function because it passes the vertical line test. The relation in the following figure is not a function because it fails the vertical line test. It has more than one y-intercept and many points at which a vertical line would cross the graph more than once. How to find the y-intercept of a functionTo find the y-intercept of a function, we need to find the point on the graph where x = 0. Given a function, f(x), the y-intercept occurs at f(0). Example Find the y-intercept of: f(x) = (x - 2)3 + 4 f(0) = (0 - 2)3 + 4 f(0) = -8 + 4 = -4 Thus, the y-intercept is at (0, -4). Download Article Download Article On their own, y-intercepts aren’t complicated at all—they’re simply points where the graph of the equation intersects with the Y-axis.[1] But how are you supposed to find a y-intercept when you only have a limited amount of info on hand? Thankfully, it’s not nearly as hard as it looks. We’ll walk you through all the major ways to find the y-intercept when you already have the slope and a point, two points, or just want to use a simple equation. With a little practice, you can make quick work of any y-intercept problem that comes your way.
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Advertisement About This ArticleArticle SummaryX To find the y intercept using the equation of the line, plug in 0 for the x variable and solve for y. If the equation is written in the slope-intercept form, plug in the slope and the x and y coordinates for a point on the line to solve for y. If you don't know the slope, calculate it by dividing the rise of the line by the run. If you want to find the y-intercept if you only know 2 points along the line, keep reading the article! Did this summary help you? Thanks to all authors for creating a page that has been read 1,120,138 times. Did this article help you? |