I was surprised to see that as expected the graph stretched by a factor of two to three by a factor of two to three. A 3 Indicates a vertical stretch by a factor of 3 and a reflection in the x-axis.
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Now here the horizontal stretch factor s 2 1 or 2 and the horizontal translation is 2.
. If 0 b 1 0 b 1 then the graph will be. Vertical compression by a factor of 19. Horizontal stretch and shrink.
Y c f x vertical stretch factor of c. The domain of both f x and g x is x. When a a is between 0 0 and 1 1.
Y x3 y x 3. This is a horizontal stretch by a factor of 3. Horizontal And Vertical Graph Stretches And Compressions Part 1 The general formula is given as well as a few concrete examples.
Y 3x -43 -3. When a a is greater than 1 1. Vertical shift 5 units down.
For example if we begin by graphing the parent function f x 2x f x 2 x we can. B 2 Indicates a horizontal compression by a factor of h 8 Indicates a translation 8 units to the left. Vertical compression by a factor of 19.
While horizontal and vertical shifts involve adding constants to the input or to the function itself a stretch or compression occurs when we multiply the parent function f x bx f x b x by a constant a 0 a 0. Stretch horizontally by a factor of 2. If b 1 b 1 then the graph will be compressed by 1 b 1 b.
Y 2 f 1 2 x 1 3. Vertical shift 6 units up. Reflect over the x-axis.
Stretched horizontally by a factor of absdfrac1a if 0ltabsalt 1text and reflected about the y-axis and stretched or compressed if alt 0text As you may have notice by now through our examples a horizontal stretch or compression will never change the y intercepts. Compare and list the transformations. Vertical stretch by 3.
Translate left 2 units. Y f cx compress horizontally factor of c. Lastly lets see the transformations done on px to reach qx.
Mai 2022 amanda setton nationality. Examples of Horizontal Stretches and Shrinks. The problem is when I use these parameters to transform a point the answer is wrong.
This is a vertical compression by a factor of 1 4. Consider the following base functions 1 f x x2 - 3 2 g x cos x. For any given output the input of g is one-third the input of f so the graph is shrunk horizontally by a factor of 3.
Lets take a look at how f x x2 will get affected by the values of 12 and 13. Click here to get an answer to your question y x2 undergoes a horizontal stretch by a factor of 13 then a shift up of 4 units. Horizontal Stretches and Compressions.
A vertical translation of 2 units down. Vertical Compression or Stretch. Vertical stretch by 3.
Reflection across the y-axis. D For 1 1 4 4 g x f x a. Some texts always use a factor greater than 1.
If g x f 3x. Given a function f x f x a new function gx f bx g x f b x where b b is a constant is a horizontal stretch or horizontal compression of the function f x f x. A horizontal stretch by a factor of 3.
A horizontal stretch by a factor of 3 A vertical stretch by a factor of 2. 1 A vertical stretch by a factor of 2 A reflection in the y-axis 4. The vertical stretch is 2 and the vertical shift is 3.
Here the factor cited is always greater than 1. Y 2 f 1 2 x 2 3. So we can isolate the x like.
Translate up 4 units. A vertical translation of 2 units up. In the function yf2z is replaced.
Reflection across the y-axis. A reflection in the x-axis. The graphical representation of function 1 f x is a parabola.
Suppose the translated function is given by. You can put this solution on YOUR website. A scale factor of 1a multiplied by x will stretch f xs graph horizontally by a factor of a.
Qx p2x 4. Horizontal stretch by a factor of 3. Hence qx results from px being compressed horizontally by a scale factor of 2 and translated 4 units downward.
Y 3x -43 -3. We can see that nx is the result of mx being stretched vertically by a scale factor of 2 and compressed horizontally by a scale factor of 3. Compressing and stretching depends on the value of a a.
Transform the function f x as described and write the resulting function as an equation. Y 1cf x compress vertically factor of c. They say that f2x is compressed by a factor of 2 meaning x is divided by 2 fx2 is stretched by a factor of 2 meaning x is multiplied by 2 In general fcx is stretched by a factor of 1c if 0 c 1 and compressed by a factor of c if c 1.
The range of both f x and g x is 0 y y. The domain of both f x and g x is x. Reflection across the x-axis.
Write the equation of an exponential function that has been transformed. A horizontal stretch or shrink by a factor of 1 k means that the point x y on the graph of f x is transformed to the point x k y on the graph of g x. Vertical shift 6 units up.
If g x 3f x. Vertical stretch by a factor of 8. However if I use the.
Vertical stretch by a factor of 8. Horizontal stretch by a factor of 3. Horizontal stretch by a factor of 3.
Horizontal compression by a factor of 14. Stretch vertically by a factor of 3. Horizontal compression by a factor of 14.
Reflection across the x-axis. Vertical shift 5 units down. As you know the transformations are gx vertical stretch factor fx - right shift vertical shift For the given transformations the equation becomes.
For any given input the output iof g is three times the output of f so the graph is stretched vertically by a factor of 3.
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