What is the range of 3cos(x)+1 ?

The range of 3cos(x)+1 is -2<= f(x)<= 4

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range of 3cos(x)+1

range

3 cos (x) + 1

- 2 \leq f (x) \leq 4

Interval Notation

[- 2, 4]

Solution steps

The range of the basic

cos

function is

- 1 \leq cos (x) \leq 1

- 1 \leq cos (x) \leq 1

Multiply the edges of the range by:

3

- 3 \leq 3 cos (x) \leq 3

Add to the edges of the range:

1

- 2 \leq 3 cos (x) + 1 \leq 4

Therefore the range is

- 2 \leq f (x) \leq 4

y = - 3 x + 2

f (x) = lo g_{10} (x - 7)

f (x) = 3 sin (2 x - \frac{π}{2})

y = 6

(x^{2} + 2)^{2} + 2