What's the range of this function y=x^2-5

Question

i do not understand if someone could help me 

Answer 1

The range of a function is the spread of possible y-values, from the minimum y-value to the maximum y-value.  The base function you have is:

 

y = x²

 

This is an upward-opening parabola with the vertex at the origin.  When you square a positive number, you get a positive number.  When you square a negative number, you also get a positive number.  Hence the range of y = x² is all y≥0.  When you subtract 5, y = x² - 5, it moves every point on the parabola down 5 units on the y-axis, so the range becomes all y ≥ -5.

 

To check, try graphing the parabola of y = x²-5.