What is the domain and range of f(x)=x^2 -3 ?

Question

Please help me with this magh problem

Answer 1

Angelique:

 

The quantity x² - 3 can be calculated for all real numbers x.  Hence the domain is the set of all real numbers.

 

The smallest value of y = f(x) = x² -3 is -3 when x= 0.  Further for any y > 3, from x² = y + 3,  x can be calculated as SQRT(y + 3). (see that for any y > -3, y+3 > 0, so we can find the square-root.  Therefore the Range is [-3, +infintiy)

 

Dr. G.

Answer 2

f(x) = x²-3

 

The domain of a polynomial is all x: (-∞,∞)

 

Since f(x) is a quadratic equation, its graph is a parabola.  Since the coefficient of the x² term is positive (1), the graph opens upward and the vertex is at the bottom and is the lowest or minimum point of f(x).  The vertex is located at the point (0,-3).  Hence the range is from -3 to infinity: [-3,∞)

Answer 3

the function is a polynomial.

there are no fractions and no square root.

So there is no limitation on the domain which is all real numbers.

 

The smallest value for x² is zero so the smallest value for x² - 3 is -3.

As x increases from zero, the function gets larger and larger so the range is y ≥ -3