The function in the graph has the name of square function.
The domain of a function is all values of x the function can have. The domain of this function is all real numbers:
[tex]\mleft\lbrace x\in\R\mright\rbrace[/tex]
The range of a function is all values of y the function can have. The range of this function is all positive numbers, including zero:
[tex]\mleft\lbrace y\in\R\mright|y\ge0\}[/tex]
In order to graph f(x) + 2, we just need to translate the graph 2 units up. To find the new points, we need to increase all y-coordinates by 2:
(-2, 6), (-1, 3), (0, 2), (1, 3), (2, 6)
Domain: {x ∈ ℝ}
Range: {y ∈ ℝ | y ≥ 2}
Then, in order to graph f(x) - 2, we just need to translate the graph 2 units down. To find the new points, we need to decrease all y-coordinates by 2:
(-2, 2), (-1, -1), (0, -2), (1, -1), (2, 2)
Domain: {x ∈ ℝ}
Range: {y ∈ ℝ | y ≥ -2}
