The figure below shows the graph of function f with domain 0

The figure below shows the graph of function f with domain [0, 2] and range [0, 1]. Determine the domain and range of the following functions. Express your answering using interval notation. 2 a, y = f(x) Domain: Preview Range: Preview b, y = f(z) + 2 Domain: Preview Range: Preview c. y = 2f(x) Domain: Range: Preview Preview d, y = f(x)-1 Domain: Preview

Solution

a. The domain of y = f (x) is [ 0, 2] . The range is [ 0,1]

b. The domain of y = f (x) + 2 is [ 0, 2] . The range is [ 2,3]

c.The domain of y = 2 f (x) is [ 0, 2] . The range is [ 0, 2]

d. The domain of y = f ( x) - 1 is [ 0, 2] . The range is [-1, 0]

e. The domain of y = - f (x) is [ 0, 2] . The range is [-1, 0]

f. The domain of y = f (x + 2) is [ 0, 2] . The range is [ f (2), f (4)] which is indeterminate as f (4) is not defined.

g. The domain of y = f (x - 1) is [ 0, 2] . The range is [ f ( -1), f (1)] which is indeterminate as f (-1) is not defined.

h. The domain of y = f (-x) is [ 0, 2] . The range is [ 0, f ( -2)] which is indeterminate as f (- 2) is not defined.

i. The domain of y = f (x + 1) + 1 is [ 0, 2] . The range is [ f (2) + 1, f (3) + 1] which is indeterminate as f (3) is not defined.