Question

Graph the functions on the same coordinate plane.f(x) = −5g(x) = x^2 + 2x − 8What are the solutions to the equation f(x) = g(x)? Select each correct answer.−5−3−113

Answer 1

`\begin{equation*} -3,1 \end{equation*}`

Step-by-step explanation

The graphical solution to the given equation is obtained at the points where the two graphs of the two functions intersect each other on the coordinate plane.

To graph f(x), we simply draw a straight horizontal line at the point y = -5.

To graph g(x), we have to find coordinate points by substituting values of x into the function and obtaining values for g(x).

Let us find the value of g(x) when x = -3, -1, 1:

`\begin{gathered} x=-3: \\ g(-3)=(-3)^2+2(-3)-8=9-6-8 \\ g(-3)=-5 \\ x=-1: \\ g(-1)=(-1)^2+2(-1)-8=1-2-8 \\ g(-1)=-9 \\ x=1: \\ g(1)=(1)^2+2(1)-8=1+2-8 \\ g(1)=-5 \end{gathered}`

Now, we have three points to plot the graph with: (-3, -5), (-1, -9), (1, -5)

Let us now plot the graphs of the functions:

Therefore, the solutions to the equation f(x) = g(x) are:

`\begin{gathered} x=-3,x=1 \\ \Rightarrow-3,1 \end{gathered}`