f(x)=x^2+7 need the domain and range of the function in interval notation

Question

f(x)=x² +7

 

need the domain and range of the interval notation

 

Answer 1

Domain: (-∞, ∞), since f(x) is defined for all real values of x.

Range: [7, ∞), since the minimum value of f(x) is 7, and f(x) is open up,  there is no upper limit.

Answer 2

Hi Jim;

The domain is negative infinity to positive infinity.  The factor of x is the numerator, not the divisor.  Therefore, it can be zero.  It is also not being square-rooted.  Therefore, it can be a negative number.

 

The range is different because x² will render any value of x either zero or a positive number.  We need to establish the minimum while recognizing there is no maximum.

y=0²+7

y=7

 

The range is...

[7, positive infinity]