Question

True or false?

The graph of y = 4sin(x + 3) - 2 is obtained by shifting the graph of y = 4sin x - 2 horizontally 3 units to the right.

Answer 1

Answer: This is false.

Explanation:

The general function equation is,

`y=a\cdot \sin b(x+c)+d`

where,

period is
`(2\pi)/(b)`,

horizontal shift or phase shift is c,

amplitude is a,

vertical shift is d.

The original equation of graph is,
`y=4\sin (x)-2`

After shifting the equation of graph is,
`y=4\sin (x+3)-2`

As per question, when we are adding 3 in original equation of graph then the graph shifted horizontally to the left by 3 units.

Answer 2

FALSE.

The effect of adding +3 to the argument of a function f(x) is to shift the original f(x) horizoantally 3 units to the left.