Question

1. Describe the two transformations that occur to the parent function f(x)=√x when transformed to the function g(x)=2√x+3.

2. Then, describe the domain and range of g(x). (You may use Interval Notation or Words)

Answer 1

1. This stretches the function in the y direction by 2 and moves the function up 3 units

2. Domain : all real numbers greater than or equal to zero

{x ∈ R : x>=0}

Range : all real numbers greater than or equal to three

{y ∈ R : g>=3}

Explanation:

f(x) = sqrt(x)

g(x) = 2 sqrt(x)

This stretches the function in the y direction by 2

h(x) = 2 sqrt(x) +3 moves the function up 3 units

2. The domain is the input values

2 sqrt(x) +3 this is limited by sqrt (x) so x>=0

Range is the output values so sqrt(x) must be o or positive

The minimum is 0+3

y >=3