Question

Find the domain and range of f(x) = |x| + cosx

A. domain: (-infinity, infinity); range: (-infinity, infinity)

B. domain: (-infinity ,1]; range: (- infinity, infinity)

C. domain: (-infinity, infinity); range: (-infinity, 1]

D. domain: (-infinity, infinity); range: [1, infinity)

Answer 1

D. domain: (-infinity, infinity); range: [1, infinity)

Explanation:

The domain is the values that x can take

The domain is (-infinity, infinity)

The range is the values that y can take

absolute value is 0 or greater

cos x is from -1 to 1

The minimum value is when x=0

The smallest value is 1 and the largest is infinity

Answer 2

D. domain: (-infinity, infinity); range: [1, infinity)

Explanation:

The domain is the values that x can take

The domain is (-infinity, infinity)

The range is the values that y can take

absolute value is 0 or greater

cos x is from -1 to 1

The minimum value is when x=0

The smallest value is 1 and the largest is infinity