What is the range of y=cos(1/2 x)+2 ?

The range of y=cos(1/2 x)+2 is 1<= f(x)<= 3

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range of y=cos(1/2 x)+2

range

y = cos (\frac{1}{2} x) + 2

1 \leq f (x) \leq 3

Interval Notation

[1, 3]

Solution steps

The range of the basic

cos

function is

- 1 \leq cos (\frac{1}{2} x) \leq 1

- 1 \leq cos (\frac{1}{2} x) \leq 1

Add to the edges of the range:

2

1 \leq cos (\frac{1}{2} x) + 2 \leq 3

Therefore the range is

1 \leq f (x) \leq 3

f (x) = 8 x^{3} + 6

y = 1 + 2^{- x}

\frac{1}{4} x^{3} - 2

f (x) = \frac{1}{5} x

f (x) = x + \frac{3}{x + 2}

What is the range of y=cos(1/2 x)+2 ?
The range of y=cos(1/2 x)+2 is 1<= f(x)<= 3