Question

3. The graph of function g(x) is shown below.

Answer 1

Explanation:

g(x) = 2*
`√(x)` + 4

Domain is the input so what limits are there to the input?

for the square root, you are told that you can't not put in negative numbers until you learn about imaginary number in the for m a+bi, but for now, just say the input is 0 to ∞, for now The domain is 0 to ∞

Range is the output

so that is from 4 to ∞

Answer 2

a. translation 2 right and up 4

b. g(x) = √(x -2) +4

c. domain: x ≥ 2; range: y ≥ 4

Explanation:

You have the graph of a square root function with its vertex at (2, 4). You want to know what transformation that represents, the equation of the graph, and the domain and range of the function.

a. Transformation

The vertex of the square root function f(x) = √x is located at (0, 0). In the given graph, it has moved to (2, 4). The vertical and horizontal scale factors remain unchanged. This transformation is ...

translation right 2 units and up 4 units

b. Equation

Translation of function f(x) by h units right and k units up gives you ...

g(x) = f(x -h) +k

Here, we have (h, k) = (2, 4), and f(x) = √x, so the transformed function is ...

g(x) = √(x -2) +4

c. Domain and Range

The domain is the horizontal extent of the graph. For a square root function it is the x-value of the vertex, and all points to the right of that.

domain of g(x): x ≥ 2

The range is the vertical extent of the graph. For a square root function it is the y-value of the vertex, and all points above that.

range of g(x): y ≥ 4