No calculator, leave in exact form. Determine the amplitude, period and phase shift of the function.

Question

Determine the amplitude, period, and phase shift of the function. Then graph one period of the function. Show your steps (basic graph and all transformations).

𝑓(𝑥)=sec(2𝑥+𝜋)+1

a.) Period

b.) Phase Shift

c.) Graph

Answer 1

𝑓(𝑥)=sec(2𝑥+𝜋)+1

it important to rewrite 𝑓(𝑥)=sec(2[𝑥+𝜋/2])+1

now you can see when x= -𝜋/2 then at zero for argument.,,, phase shift is -𝜋/2

when does 2x=2𝜋 ,,,, that is period

amplitude is coefficient in front of sec so that is 1

the +1 is a translation of sec(2[𝑥+𝜋/2]) up 1