The initial value is the output that is paired with the least input.
Initial value of f(x): 172 Initial value of g(x): 14 Range of f(x): 112 ≤ f(x) ≤ 172 Range of g(x): 9 ≤ g(x) ≤ 14
Practice makes perfect
Let's compare the initial value first and then the range for each of the linear functions f(x) and g(x).
Initial value
The initial value is the output that is paired with the least input. We have been given the domain for the functions.
Domain: 2≤ x≤ 6
Therefore, we know that the least input for f(x) and g(x) is 2. From the table, we can see that the output which is paired with 2 for g(x) is 14. To find the initial value of f(x), we can substitute 2 for x in its rule!
Since g(x) is a decreasing linear function and its domain is the set of all real numbers from 2 to 6, its range will be the set of all real numbers from g(6) to g(2).
g(6) ≤ g(x) ≤ g(2)
From the table, we can see that g(6)=9 and g(2)=14. We can write its range.
Range of $g(x)$:& 9 ≤ g(x) ≤ 14
The same happens with f(x). It is a decreasing linear function whose domain is the set of all real numbers from 2 to 6. Hence, its range will be the set of all real numbers from f(6) to f(2).
f(6) ≤ f(x) ≤ f(2)
We already know that f(2)= 172. To find f(6), let's substitute x=6 in its rule!
