Respuesta :
The first function is a linear function while the second function is neither a linear nor exponential
How to identify whether a function is linear, exponential, or neither?
A linear function is of the form f(x) = mx + c,
where m is the slope (or rate of change) and y-intercept
m = y2-y1 / x2-x1
An exponential function is of the form f(x) = abˣ
where a and b are constants
In a linear function, the slope must be constant. Also, in exponential function a and b must be constants
Given:
(x) 2 3 4
F(x) 5.5 7 8.5
For x = 2 and 3:
slope = 7-5.5 / 3-2 = 1.5
For x = 3 and 4:
slope = 8.5-7 / 4-3 = 1.5
The slope is the same, thus, it is a linear function
Note: f(x) = y
(x) 0 2 4
F(x) 2 5 9
This is not linear, check for exponential
y = abˣ
when x = 0, y =2
2 = ab⁰
a = 2
when x =2, y = 5
5 = 2b²
b² = 5/2
b = √(5/2)
when x =4, y = 9
9 = 2b⁴
b⁴ = 9/2
b = [tex]\sqrt[4]{(9/2)}[/tex]
Since the b are not the same. Thus, this is an exponential function also
Learn more about exponential function on:
brainly.com/question/27161222
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