Linear function f with f(-3) = 1 and f(13) = 5 is given by [tex]\rm f(x) = \dfrac{1}{4}x + \dfrac{7}{4}[/tex] and this can be determined by using the given data.
Given :
f(-3) = 1 and f(13) = 5.
The generalised linear function is given by:
f(x) = ax + b --- (1)
Now, it is given that (f(-3) = 1) that means at (x = -3) the above function is equal to 1.
f(-3) = a(-3) + b
1 = -3a + b
b = 1 + 3a ---- (2)
Now, it is also given that (f(13) = 5) that means at (x = 13) the function (f(x) = ax + b) is equal to 5.
f(13) = 13a + b
5 = 13a + b
Now, put the value of 'b' in the above equation.
5 = 13a + 1 + 3a
4 = 16a
[tex]\rm a = \dfrac{1}{4}[/tex]
Now, put the value of 'a' in equation (2).
[tex]b = 1 +3\times \dfrac{1}{4}[/tex]
[tex]b = \dfrac{7}{4}[/tex]
Now, put the value of a and b in equation (1).
[tex]\rm f(x) = \dfrac{1}{4}x + \dfrac{7}{4}[/tex]
For more information, refer to the link given below:
https://brainly.com/question/21835898
