Vertical compression question

In summary, the new equation g(x) after a vertical compression by a factor of 1/2 is g(x) = (x^2)-2.
  • #1
dragon513
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0
Q. Given f(x)=2(x^2)-4 , determine the new equation g(x) after a vertical compression by a factor of 1/2.

The answer provided by the book is g(X) = (x^2)-2, but shouldn't it be g(x) = (x^2)-4 ?

Help will be much appreciated.

Regards,

Adam
 
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  • #2
dragon513 said:
Q. Given f(x)=2(x^2)-4 , determine the new equation g(x) after a vertical compression by a factor of 1/2.

The answer provided by the book is g(X) = (x^2)-2, but shouldn't it be g(x) = (x^2)-4 ?

Help will be much appreciated.

Regards,

Adam
No, the book's solution is correct. Horizontal changes are changes in x, vertical changes are changes in y. Since this is a vertical compression by 1/2, first calculate y= 2x2- 4, the calculate (1/2)y= (1/2)(2x2- 4)= x2- 2 (becareful to use the "distributive law"- multiply both parts by 1/2). The new y is y= x2- 2.
 
  • #3


Hello Adam,

Thank you for reaching out. It seems like there may be a mistake in the answer provided by the book. When a function is vertically compressed by a factor of 1/2, it means that the output values (y-values) are multiplied by 1/2. In this case, the original function f(x) = 2(x^2) - 4 would become g(x) = 1/2(2(x^2) - 4) = (x^2) - 2. Therefore, the correct answer should be g(x) = (x^2) - 2. I hope this clarifies any confusion. If you have any further questions, please don't hesitate to ask. Keep exploring and learning!


Scientist
 

1. What is vertical compression?

Vertical compression is a mathematical concept that describes the process of shrinking or compressing a graph vertically. It is also known as vertical scaling.

2. How is vertical compression different from horizontal compression?

Vertical compression involves changing the positions of the points on a graph along the y-axis, while horizontal compression involves changing the positions of the points along the x-axis. In other words, vertical compression affects the height of the graph, while horizontal compression affects the width.

3. What causes vertical compression?

Vertical compression can be caused by multiplying the function by a fraction or decimal that is less than one. This will result in a graph that is shorter and narrower compared to the original graph.

4. How can I identify vertical compression on a graph?

On a graph, vertical compression can be identified by a narrower shape and lower height compared to the original graph. The points on the graph will also be closer together along the y-axis.

5. What are the effects of vertical compression on a function?

Vertical compression can have several effects on a function. It can change the slope of the graph, the location of the vertex, and the domain and range of the function. It can also make the function steeper and more narrow.

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