Question

The graph below shows three functions: Graph of function f of x equals 0.5 to the power x. Graph of function g of x is a line segment with holes at endpoints connecting negative 1.8, negative 3 and 1, 3.8. Graph of p of x is a line segment connecting negative 1.7, 2.3 and 1, negative 4.2. Which function has all real numbers as its domain? Only f(x) Both g(x) and p(x) Both f(x) and g(x) Only p(x)

Answer 1

f(x)= 0.5^x has all real numbers as its domain

Explanation:

We have three functions:

f(x)= 0.5^x while g(x) and p(x) are line segments

g(x) is a line segment which passes through the two points (-1.8,-3) and ( 1,3.8)

Its domain will be the ends points. so domain of the function g(x) will be [-1.8, 3.8] which is the subset of real numbers.

Like wise domain of function p(x) will be [1.7, 1], which is also the subset of real numbers.

But when we look at f(x) it has all the possible value of x. Thus we can say that f(x)= 0.5^x has all real numbers as its domain.