Question

Can someone please help me?

Answer 1

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: $y=4x^2+2$

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

$y=4(0)^2+2=2$

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: $\frac{dy}{dx} =5$

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.