Question

The graph of a function increases twice as much over each subsequent equally sized interval. Which of the following could be the parent function of the graphed function?

Answer 1

I hope this helps you





square root of (4x+41)=x+5



4x+41>=0



x >= -10.25



(square root of4x+41)^2=(x+5)^2




4x+41=x^2+10x+25



x^2+6x-16 =0



x +8



x -2



(x+8)(x-2)=0




x= -8



x= 2 extraneous

Answer 2

The correct option is 1.

Explanation:

The given equation is

`√(4x+41)=x+5`

Taking square on both the sides.

`4x+41=(x+5)^2`

`4x+41=x^2+10x+25`
`[\because (a+b)^2=a^2+2ab+b^2]`

`0=x^2+10x+25-4x-41`

`0=x^2+6x-16`

`0=x^2+8x-2x-16`

`0=x(x+8)-2(x+8)`

`0=(x+8)(x-2)`

`x=2,-8`

Check the equation by x=2.

`√(4(2)+41)=2+5`

`√(49)=7`

`7=7`

LHS=RHS, therefore x=2 is not an extraneous solution.

Check the equation by x=-8.

`√(4(-8)+41)=-8+5`

`√(9)=-3`

`3=-3`

LHS≠RHS, therefore x=-8 is an extraneous solution.

Therefore option 1 is correct.