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)

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}

Step-by-step 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

let's solve your equation step-by-step.

4x+2=2x+12

step 1: subtract 2x from both sides.

4x+2−2x=2x+12−2x

2x+2=12

step 2: subtract 2 from both sides.

2x+2−2=12−2

2x=10

step 3: divide both sides by 2.

2x

2

=

10

2

x=5

step-by-step explanation:

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: