Question

Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph.

Answer 1

Answer:

Option d

Step-by-step explanation:

If the graph of the function $y=cf(x) +b$  represents the transformations made to the graph of $y= f(x)$  then, by definition:

If  $0$ then the graph is compressed vertically by a factor c.

If  $|c| > 1$ then the graph is stretched vertically by a factor c.

If $c$  then the graph is reflected on the x axis.

If $b> 0$ the graph moves vertically upwards.

If $b$ the graph moves vertically down

In this problem we have the function $y=cscx -9$ and our parent function is $y = cscx$

therefore it is true that $c =1$  and $b =-9 < 0$

Therefore the graph of $y=cscx$ is not stretched vertically and is not reflected.  however as $b$ then the graph moves vertically 9 units down. Observe the image

The answer is "vertical translation down 9 units"