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

a) horizontally stretch the graph of f (x) by a factor of 30

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

c) vertically stretch the graph f (X) by factor of 30

d) vertically compressing the graph of f (x) by factor of 30

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