horizontal compression equation examples

Horizontal compression equation examples how to#

Which of the following is the correct expression for g(x)?Ī.

The function, g(x), is obtained by horizontally stretching f(x) = 8x by a scale factor of 1/4. Being able to master the technique of horizontally stretching graphs can help us graph functions faster and understand their behavior.Īre you ready to test your knowledge? Let’s go ahead and try out some of these problems! Let’s always go back to these five-pointers when in doubt. Given a point (m, n), it becomes (am, n) when stretched horizontally.The resulting function will have the same range but may have a different domain.When f(x) is stretched horizontally to f(ax), multiply the x-coordinates by a.We can only horizontally stretch a graph by a factor of 1/a when the input value is also increased by a.Here are some important pointers to remember when answering problems and graphing functions that involve horizontal stretches: Summary of horizontal stretch definition and properties Ready to graph more functions and apply horizontal stretches? Let’s summarize what we have learned so far first before we try out more questions. The graph shown above confirms this, and we can apply the same process when horizontally stretching the graphs of other functions. To attain y = |x/3|, we stretch the parent function y = |x| by a factor of 3. Let’s use the table of values shown in the previous section to graph both y = |x| and y = |x/3| to visualize the effects of a horizontal stretch on a graph.Īs we have discussed, we’re expecting the graphs to stretch along the base with the values for y remaining constant. See if the coordinate points are scaled correctly as well.Make sure to double-check critical points on the graph, such as its intercepts, maximum points, and more.Since the y-coordinates will remain the same, the y-intercept stays the same as well.Only stretch the base of the graph horizontally so that the y-coordinates would remain in the same position.Before we start stretching functions horizontally by a certain factor, remember these pointers to stretch graphs faster horizontally: Now that we’ve learned about horizontal stretches and how they affect a base function, it’s time that we apply these on functions’ graphs. What does this mean for the coordinates of the new function’s graph? If the function f(x) passes through (m, n) and is stretched horizontally by a factor of 1/a, the new function will pass through (am, n). When we do this, the output values will remain the same. We also expect all its x-coordinates to increase by 3. Why don’t we compare some values from both functions? x Let’s say we have f(x) = |x|, if this function’s graph is to be stretched horizontally to attain g(x), the new function’s expression can be expressed as |1/3 ∙ x| = |x/3|. Horizontal stretch on other functions will exhibit similar properties. The graph only stretches away from the y-axis when we horizontally stretch a graph. Notice how the y-values remain the same? This is true for all horizontal stretches. Let’s go ahead and look at how f(x) = x 2 will be affected by a scale factor of 1/2 and 1/3.Īs we have expected, the graph stretches by a factor of 2 and 3. What does this mean for functions such as f(x)? When 1/a is multiplied to x, f(x)’s graph stretches horizontally by a scale factor of a. We can apply horizontal stretch to a function by multiplying its input values by a scale factor, a, where 0 < 1/a < 1. These linked articles may help you refresh your knowledge, and when you’re ready, let’s go ahead and learn more about horizontal stretching. Review how we apply vertical stretches.Refresh your knowledge of vertical and horizontal transformations.Understanding the common parent functions we might encounter.Make sure to review your knowledge of parent functions, translations, and vertical stretches before moving to the next section.

Horizontal compression equation examples how to#

We can also learn how to speed up graphing new functions based on the scale factors applied. Learning how we can stretch graphs horizontally can help us understand the family of functions’ graphs. Horizontal stretches happen when a base graph is widened along the x-axis and away from the y-axis.

Horizontal stretches are among the most applied transformation techniques when graphing functions, so it’s best to understand its definition. These functions may have been horizontally stretched using a base function. You may already have encountered graphs that look alike but share different widths. Horizontal Stretch -Properties, Graph, & Examples