How do you find the domain and range of #f(x)=sqrt(x+4)#?

Question

Isaiah Anthony · Accepted Answer

Domain = #[-4,oo)#
Range = #[0,oo)# All x values are allowed in the domain; values that result in division by zero or the taking of even square roots of negative numbers are not allowed. Clearly in this case hence the domain is all real x values greater than or equal to -4., that is #Dom_f=[-4;oo)# The corresponding range is then all the possible y values allowed as outputs and is clearly #[0,oo)# This is further confirmed by the graph: sqrt(x+4) [-11.97, 33.66, -9.85, 12.95]} is the graph.

Savannah Anderson · Answer

undefined To find the domain of $ f(x) = \sqrt{x + 4} $, we need to determine the values of $ x $ for which the function is defined. Since the square root function is only defined for non-negative values, the expression $ x + 4 $ must be greater than or equal to zero. Thus, the domain is $ x \geq -4 $.

To find the range, we need to determine the possible output values of the function. Since the square root function outputs non-negative values, the range of $ f(x) $ is all real numbers greater than or equal to zero. Therefore, the range is $ f(x) \geq 0 $.