Question

Graph the functions f(x) = -2x -6 and g(x) = -2^x - 6 on the same coordinate plane. What are the solutions of the equation -2x - 6 = -2^x - 6 Select each correct answer

A. -1
B. 0
C. 1
D. 2
E. 3

Answer 1

The answer is C and D, since x = 1, 2

Answer 2

Option C and D

Explanation:

Given : Graph of the functions
`f(x) = -2x -6` and
`g(x) = -2^x - 6` on the same coordinate plane.

To find : What are the solutions of the equation
`-2x - 6 = -2^x - 6`

Solution :

When we graph the two functions the intersection point is the solution of the function.

(The graph is attached below.)

The intersection points are (1,-8),(2,-10)

So, The solution for x is 1 and 2

Therefore, Option C and D are the correct answer.

We can verify by putting the values in the function.

`-2x - 6 = -2^x - 6`

Put x=1

`-2(1)- 6 = -2^(1)- 6`

`-2 - 6 = -2 - 6`

`-8= -8` verified

Put x=2

`-2(2)- 6 = -2^(2)- 6`

`-4 - 6 = -4 - 6`

`-10= -10` verified