Question

Please help me with this question, I am trying to help my son with this problem because its giving him that it might be multiple answer choices I can only see one pleased help.Graph the functions f(x)=−6x+2 and g(x)=−2x^+2 + 6 on the same coordinate plane. What are the solutions of the equation −6x+2=−2x^+2 +6 ?Select each correct answer. x = 0x = 1x = 2x = 3x = 4

Answer 1

The given functions are:

`\begin{gathered} f(x)=-6x+2 \\ g(x)=-2^(x+2)+6 \end{gathered}`

It is required to graph the functions, and then find the solutions of the equation:

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

To find the solution to the equation, it is sufficient to find the points of intersection of the drawn graphs. The x-coordinate of these points of intersection is the required solution.

We will start by using points to graph the equations:

Find some values of the function f(x)=-6x+2.

For x=0, substitute x=0 into the function:

`f(0)=-6(0)+2=0+2=2`

It follows that a point on the graph is (0,2).

For x=1, substitute x=1 into the function:

`f(1)=-6(1)+2=-6+2=-4`

Hence, another point on the graph of f(x) is (1,-4).

For x=2, substitute x=2 into the function:

`f(2)=-6(2)+2=-12+2=-10`

Hence, a third point on the graph is (2,-10).

Plot these points on a graph as shown:

Join these points to draw the graph of f(x):

Using the same procedure as in the first function, that is finding points for some x-values, the graph of g(x) is shown in purple:

Locate the points of intersection of the graphs of f(x) and g(x):

The points of intersection labeled are (0,2) and (2,-10).

The x-coordinates of the points (0,2) and (2,-10) are the solutions of the equation, that is, x=0, x=2.

The solutions of the given equation are x=0 and x=2.