Question

Hi, what is the domain and range of y=sec(x)+2

Answer 1

well, its not cos(x) + 2

Answer 2

sec rides the humps of the cosine function .... and since its defined as 1/cos, its undefined whenever cos is equal to zero

Answer 3

right so the angles where cos(x) = 0 will give you the vertical asymptotes or domain restrictions of sec(x)
range is basically everything outside of range of cos
range of cos(x) is [-1,1] so range of sec(x) is (-inf,-1] U [1,inf)
sec(x)+2 shifts y-values up 2, so justshift range up 2 --> (-inf,1]U[3,inf)

Answer 4

i have to add
"sec rides the humps of the cosine" is just hilarious