In the app below, select the property that you want to explore, then follow the instructions.[br][br]The small points on the function graph allow you to change its shape.
We know that:[br]- polynomials exist for any value of the variable[br]- fractions exist if their denominators are non-zero[br]- roots with an even index exist if their radicands are non-negative[br]- roots with an odd index exist for all values of the radicand[br][br]If the analytical expression of a function contains more "parts" that need conditions to exist, then the function exists for all values of the variable that satisfy all these conditions.
Do the functions [math]f\left(x\right)=\sqrt{x^2+5x+6}[/math] and [math]g\left(x\right)=\frac{1}{\sqrt{x^2+5x+6}}[/math] have the same domain?[br]Explain your conjecture, than calculate the domain(s) of [math]f\left(x\right)[/math] and [math]g\left(x\right)[/math].
What is the domain of [math]h\left(x\right)=\left|x+7\right|+1[/math]?[br]And the range?