Sketch the graph of the function f. Find the domain and range of the function. g (x) = 4 - √(x) ​

Question

Sketch the graph of the function f. Find the domain and range of the function.




`g (x) = 4 - √(x)`

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Answer 1

D: x > 0

R: g(x) ∈R

Explanation:

g(x) is a transformation of the baseline function, √x, so we can start by simply considering the function, √x;

First thing is you cannot square root a negative numbers (unless you consider imaginary numbers, but these are not real);

This limits the domain to x > 0;

As x approaches ∞ so does √x so the range is not limited;

This means the range of √x is simply all real numbers (i.e. ∈R);

The transformation of √x that gives g(x) consists of a reflection in the x-axis and an upward translation of 4 units;

These don't affect the domain or range so they are the same as for √x