Question

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

Answer 1

Answer:

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

Step-by-step 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 $0$ then the graph is compressed vertically by a factor a.

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

If $c$ 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

$c = -7\\\\|-7|> 1\\\\-7$.

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