Question

Which equation represents the graph of y = cos x flipped across the x-axis then shifted vertically up by 2 units? A.y = cos(-x) + 2 B.y = cos(x - 2) C.y = -cos x + 2 D.y = -cos x - 2

Answer 1

The resulting function after these transformations is given by:

`y=-\cos x+2`

option: C is correct.

Explanation:

We are given a equation of the parent function as:

`y=\cos x`

We are asked to find the equation of the which represents the graph of y = cos x flipped across the x-axis then shifted vertically up by 2 units.

We know that if any function
`y=f(x)` is flipped across x-axis then the equation of resulting function is:

`y=-f(x)`

Also if any function g(x) is shifted vertically up by a units then the equation is given by:

`g(x)=g(x)+2`

Hence, here the resulting function after these transformations is given by:

`y=-\cos x+2`

Hence, option: C is correct.

Answer 2

y = cos x
After flipping a cross the x-axis
∴ y = - cos x
After shifting vertically up by 2 units
∴ y = - cos x +2

the correct answer is option C
C.y = -cos x + 2

See the attached figure