Question

14. Compare the graph below to the function

Answer 1

Option (2)

Explanation:

Parent function has been given as,

f(x) =
`√(x)`

When translated by 3 units left,

f(x + 3) =
`√((x+3))`

g(x) =
`√((x+3))`

If the translated function is stretched vertically by a scale factor = k

New function will be,

g'(x) =
`k√((x+3))`

Since a point (1, 4) passes lies on the transformed function.

g'(1) =
`k√((1+3))`

4 = 2k

k = 2

Therefore, transformed function represents the translation by 3 units in the negative side of the x-axis and stretched vertically by 2 units.

Option (2) will be the answer.