Answer:
(1)
First transformation:
f(x) is shifted upward by 3 units
Second transformation:
f(x) is vertically stretched by 2 units
(2)
Domain:
[tex][0,\infty)[/tex]
Range:
[tex][3,\infty)[/tex]
Step-by-step explanation:
we are given function as
[tex]f(x)=\sqrt{x}[/tex]
[tex]g(x)=2\sqrt{x}+3[/tex]
(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
[tex]g(x)=2\sqrt{x}+3[/tex]
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,
[tex]x\geq 0[/tex]
so, domain will be
[tex][0,\infty)[/tex]
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
[tex][3,\infty)[/tex]
