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

the answer is a

step-by-step explanation:

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.