In this case, f( x) is undefined when the denominator is zero, which means: Now we can plot the points from the table, with the asymptote at the undefined spot.Īsymptote time. The graph will approach it but never cross it. So there is no x-intercept.īut once again, the x-axis acts as a horizontal asymptote.
But in this case, the numerator is simply 5. We find the x-intercept by setting the numerator equal to zero. We find the y-intercept by evaluating f(0). Let's sketch a dotted vertical line right there. In this case, f( x) is undefined for x = 4. Let's add a few more points to our table.įind any asymptotes by checking for x-values that turn the denominator into zero. Hmmmm, something tells us that we don't have enough information to finish the graph. Let's make a table to get a few more points. The graph approaches the x-axis but will never touch it. However, the x-axis does act as a horizontal asymptote.
In this case, f( x) is undefined for x = 0. Sample Problemįind any asymptotes by checking for which values make the denominator equal to zero. Once we have our asymptotes and intercepts, we dig up other points we'll need to draw the rest of the graph.įair warning: these guys are gonna have some pretty weird shapes when we graph them. That tells us where our function hits the x-axis. We find the x-intercept of the function by setting the numerator equal to zero. We find the y-intercept of the function by solving for f(0), which tells us where the curve hits the y-axis. Intercepts also help us in our graphing endeavors. (Remember that no-no?) We draw vertical asymptotes as dotted vertical lines, and our curve shouldn't ever quite hit those dotted lines. Vertical asymptotes happen wherever the denominator is zero, which makes the fraction undefined. The graph will just get closer and closer to the asymptote. To translate from math-speak, an asymptote is an imaginary line that a graph approaches but never touches. If we get a big, fat "undefined" for a specific value of x, that shows us where the graph's asymptotes are. If we find that f(0) = 2, for example, that means the point (0, 2) is on our graph. When we evaluate a function for specific values, we're finding an ordered pair (think Tweedle Dee and Tweedle Dum, Mary Kate and Ashley, peanut butter and jelly). Graphing rational functions is not rocket science, and it won't break the bank (unlike that last purchase-a sweet ukulele). Don't worry if the last time you graphed something was when you were tracking the life and hard times of your ever-shrinking bank account.
0 kommentar(er)
