Question

HELP!! Needed for algebra two!

Write equations that represent the transformed functions described below:
(a) f(x) =√x is shifted left 4 units and vertically compressed by a factor of
`(1)/(3)` or 1/3
(b) f(x) =√x is vertically stretched by a factor of 4 and then shifted 3 units up
(c) f(x) =√x is shifted left 2 and then shifted 6 units down

Answer 1

a. g(x) = (1/3)√(x + 4)

b. g(x) = 4√x + 3

c. g(x) = √(x + 2) - 6

Explanation:

(a) To shift the graph of f(x) = √x left 4 units, we need to replace x with (x + 4). To vertically compress the graph by a factor of 1/3, we need to multiply the entire function by 1/3. Therefore, the transformed equation is:

g(x) = (1/3)√(x + 4)

(b) To vertically stretch the graph of f(x) = √x by a factor of 4, we need to multiply the entire function by 4. To shift the graph 3 units up, we need to add 3 to the function. Therefore, the transformed equation is:

g(x) = 4√x + 3

(c) To shift the graph of f(x) = √x left 2 units, we need to replace x with (x + 2). To shift the graph 6 units down, we need to subtract 6 from the function. Therefore, the transformed equation is:

g(x) = √(x + 2) - 6