Question

Consider the three functions: f(x) = (4)x g(x) = (4)–x h(x) = –(4)x Which statements are true about the domain and range of f(x), g(x), and h(x)? Check all that apply. f(x) has a domain of all real numbers. g(x) has a range of y < 0. h(x) has a range of y > 0. g(x) has a domain of all real numbers. h(x) has a domain of x > 0.

Answer 1

1. Functions of the form f(x)=ax+b, where a is non zero, are called "linear functions" and the graphs of them are inclined lines.

2. If a>0, the line is increasing, so it gets higher as we move x to the right

If a<0, the line is decreasing.

3. There is no x we are not allowed to plug in the function: so Domain = all Real numbers

4. Since the lines are either increasing or decreasing, f(x), represented by the y values, take all values from -∞ to +∞. So Range = all Real numbers.

f(x)=4x  (increasing line, 4>0)      ,
g(x)=-x+4, h(x)=-4x  (decreasing lines, -1<0, -4<0)

all f, g, h have Domain AND Range : All real numbers

Answer 2

Answer: A, D

Step-by-step explanation:

f(x) has a domain of all real numbers.

g(x) has a domain of all real numbers.