In short: Lines that go up and down and side to side Horizontal lines go from left to right and have no slope. Vertical lines have a slope that goes up and down for no reason. Horizontal line graphs are made of lines that go across the x-axis. Line graphs that go up and down are perpendicular to the y-axis.

The best way to keep important papers off your desk, organized, and in one place is to use filing cabinets with hanging file folders. In a modern workplace, they might seem a little “old school.” This piece of furniture has been around for a long time, but it still helps us keep track of backup documents and paperwork that isn’t digital. If papers are thrown carelessly into the cabinet or not put in the right folders, that big piece of metal is just taking up space.

An asymptote is not a part of the graph, but it helps decide what to do or what shape something should be. Asymptotes that go straight up indicate that the function has no domain. Set the denominator of the fraction to zero to find the equation of the vertical asymptotes. On the other hand, horizontal asymptotes show what happens to the curve when the x values get very big or very small. To find a horizontal asymptote, you have to look at the degree of the polynomials in both the numerator and the denominator.

Some graph expressions for functions go from minus infinity to plus infinity. But this isn’t always true; some functions stop at a point of discontinuity or end before they reach a certain spot on the graph. Asymptotes are straight lines that show how close a function gets to a certain value if it doesn’t keep going in opposite directions to infinity. Asymptotes that go up or down always follow the formula x = C, while asymptotes that go left or right always follow the formula y = C, where C is a constant. If you follow a few simple steps, it’s easy to find asymptotes, whether they are horizontal or vertical.

If a graph is horizontally compressed, the new function will need less x-values than the original function to map to the same y-values. If the graph is stretched horizontally, it will need more x-values to map to the same y-values as the original function.

Transformations of exponential graphs work the same way as other functions. Like other parent functions, the parent function [latex]fleft(xright)=bx[/latex] can be changed using shifts, reflections, stretches, and compressions without losing its shape. For example, the exponential function keeps its basic shape no matter how it is changed, just like the quadratic function does when it is moved, reflected, stretched, or compressed.