We want to answer some different things about linear functions. The answers are:
- 1) D: 0 ≤ x ≤ 3, x ∈ R
- 2) D: 0 ≤ x ≤ 5, x ∈ R
- 3) f(0) = 2
- 4) g(0) = 0
- 5) R: 2 ≤ f(x) ≤ 5
- 6) R: 0 ≤ g(x) ≤ 10.
Working with linear functions
First, we want to get the domain of the two shown functions, we define the domain as the set of possible inputs of the functions.
1) For f(x) we know that the domain is the set of all real numbers included between the smallest and largest values in the table, so the domain of f(x) is:
D: 0 ≤ x ≤ 3, x ∈ R
2) Now we can do the same for g(x), here we need to look at the graph of g(x). We can see that it starts at x = 0 and ends at x = 5, then the domain is:
D: 0 ≤ x ≤ 5, x ∈ R
3) The initial value of f(x) is just f(x) evaluated in 0, so we have:
f(0) = 2 (from the table)
4) The initial value of g(x) is g(x) evaluated in x = 0, by looking at the table we can see that:
g(0) = 0.
5) The range of a function is the set of possible outputs, given that these are linear equations, to get the range we just need to evaluate the functions in both ends of the domain.
for f(x) we have:
So the range is R: 2 ≤ f(x) ≤ 5
6) Similar to above, here we can see that:
So the range of g(x) is R: 0 ≤ g(x) ≤ 10.
If you want to learn more about linear functions, you can read:
https://brainly.com/question/4025726
