Question

The graph of the function f(30x) can be obtained from the graph of y=f(x) by one of the following actions:

Answer 1

Answer:

Horizontally compress the graph of f(x) by a factor of 30 ⇒ answer b

Step-by-step explanation:

* Lets revise the vertical and horizontal stretching or compressing

 a graph

- A vertical stretching is the stretching of the graph away from the

 x-axis  

- If k > 1, then the graph of y = k•f(x) is the graph of f(x) vertically  

 stretched by multiplying each of its y-coordinates by k  

- A vertical compression is the squeezing of the graph toward  

 the x-axis.  

- If 0 < k < 1 , then the graph of y = k•f(x) is the graph of f(x)

vertically

 compressed by multiplying each of its y-coordinates by k

- A horizontal stretching is the stretching of the graph away from

 the y-axis

- If 0 < k < 1 , then the graph y = f(k·x) is the graph of f(x) horizontally

 stretched by dividing each of its x-coordinates by k

- A horizontal compression is the squeezing of the graph toward

 the y-axis.

- If k > 1, then the graph of y = f(k•x) is the graph of f(x) horizontally

 compressed by dividing each of its x-coordinates by k.

* Lets solve the problem

- The graph of the function f(30 x) can be obtained from the

   graph of y = f(x)

∵ x multiplied by 30

∴ f(x) is stretched or compressed horizontally

- If the factor greater than 1 then the graph compressed

∵ 30 > 1

∴ f(x) is compressed horizontally by scale factor 30 to obtained

  the function f(30 x)

* Horizontally compress the graph of f(x) by a factor of 30