Question

Please help me with this. Idk how to do it and today is my last day to complete it.

Answer 1

(1)

First transformation:

f(x) is shifted upward by 3 units

Second transformation:

f(x) is vertically stretched by 2 units

(2)

Domain:

`[0,\infty)`

Range:

`[3,\infty)`

Explanation:

we are given function as

`f(x)=√(x)`

`g(x)=2√(x)+3`

(1)

We can see that 3 is added to y-value

so, f(x) is shifted upward by 3 units

and 2 is multiplied to y-value

so,

f(x) is vertically stretched by 2 units

First transformation:

f(x) is shifted upward by 3 units

Second transformation:

f(x) is vertically stretched by 2 units

(2)

we are given

`g(x)=2√(x)+3`

Domain:

we know that

domain is all possible values of x for which any function is defined

Since, it is sqrt function

so, value inside sqrt is always positive

so,

`x\geq 0`

so, domain will be

`[0,\infty)`

Range:

we know that

range is all possible values of y for which any function is defined

Since, it is sqrt function

so, value of sqrt is always positive

so, smallest y-value is 3

so, range will be

`[3,\infty)`