Question

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

y= -7 sec x

Answer 1

Option c. Reflection across the x-axis and vertical stretch by a factor of 7

Explanation:

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

If
`0 <c <1` then the graph is compressed vertically by a factor a.

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

If
`c <0` then the graph is reflected on the x axis.

In this problem we have the function
`y = -7secx` and our paretn function is
`y = secx`

therefore it is true that

`c = -7\\\\|-7|> 1\\\\-7 <0`.

Therefore the graph of
`y = secx` is stretched vertically by a factor of 7 and is reflected on the x-axis

Finally the answer is Option c