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?

Answer 1

Answer:   f(x)= $0.5^x$ has all real value as its domain.

Explanation: since, we have three functions f(x)=$0.5^x$,

while g(x) and p(x) are line segments.

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

Thus it is clear that 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 set (R).

Similarly, domain of function p(x) will be [1.7, 1], which is also the subset of R.

But, when we talk about f(x) it contains all the possible value of x. Thus we can say that $f(x)= 0.5^x$ has R as its domain.

Answer 2

p(x) contains all real numbers as its domain because both of the other functions are only line segments and cover a finite interval of x.