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

Answer:

Option C and D

Step-by-step 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