Question

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

y= -7 sec x

Answer 1

The answer is (c)

Explanation:

* Lets study the problem

∵ The basic function is y = sec(x)

∵ y = -7 sec(x)

∴ It is a vertical stretch or compression because y is multiplied by -7

* Lets revise the vertical stretched and compression

- If the function is f(x), and a new function is g(x) = a f(x)

- Then there is a vertical stretch or vertical compression

of the function f(x)

# If a > 1, then the graph will be stretched.

# If 0 < a < 1, then the graph will be compressed.

# If a < 0, then there will be combination of a vertical stretch

or compression with a vertical reflection.

∵ a = -7 ⇒ a < 0 and I-7I = 7 > 1

∴ There is a combination between vertical stretching and

vertical reflection

* That means there is a reflection across the x-axis and

vertical stretch by scale factor = 7