Option A:
Function B is a non-linear function and Function A is a linear function.
Option C:
Function A has only one x-intercept.
Solution:
Function A: The function represented by the table is y = 5x.
Function B: [tex]y=4x^2+2[/tex]
Option A: Function B is a non-linear function and Function A is a linear function.
A function which is in the equation of a straight line form is a linear function.
Otherwise it is non-linear function.
Linear equation form: y = mx + c
It is clear that function B is non-linear because it has square term and function A is linear function.
The option A is true.
Option B: Function B has two y-intercepts at (0, 2) and (0, –2).
Substitute x = 0 in function B, we get
[tex]y=4(0)^2+2=2[/tex]
So, function B has only one y-intercept.
The option B is false.
Option C: Function A has only one x-intercept.
Substitute y = 0 in function A, we get
(0) = 5x
⇒ x = 0
Hence function A has only one x-intercept.
The option C is true.
Option D: Function A has a negative rate of change and Function B has a positive rate of change.
Function A: y = 5x
Rate of change of function A: [tex]\frac{dy}{dx} =5[/tex]
It is positive.
The option D is false.
Hence the true statements are
Function B is a non-linear function and Function A is a linear function.
Function A has only one x-intercept.
