Question

9-11-20Provide a complete written response to the prompts. You must include any graphs or sketchesthat apply1. Explain how the points of intersection of graphs of functions can be determined (orverified) using the multiple representations of a system of equations. Provide examples anda sketch.I.Chrome OS

Answer 1

Each function is represented by a certain expression, it usually has the form of "f(x) = expression", we can use the variable "y" in place of "f(x)", that way we will have two variables. If we have two functions, then there will be two expressions and two variables. The point where these two functions interesect is a valid solution for both expressions at the same time, so if we solve the system of equation formed by them we will find its intersection point.

Example: There are two functions "f(x) = 2*x + 3" and "h(x) = -2*x - 3". Drawing them we realize there is a point of intersection as shown below.

To calculate this point we need to solve the system of equations formed by both functions.

`\left\{ \begin{aligned}y=2x+3 \\ y=-2x-3\end{aligned}\right.`

Arranging all the variables to the left side gives us:

`\left\{ \begin{aligned}y-2x=3 \\ y+2x=-3\end{aligned}\right.`

If we sum both equations we can eliminate the "x" variable and find the value of "y".

`\begin{gathered} y+y-2x+2x=3-3 \\ 2y=0 \\ y=0 \end{gathered}`

Using the found value of "y" in either expressions results in finding the value of x.

`\begin{gathered} 0\text{ = 2x + 3} \\ x\text{ = -}(3)/(2) \end{gathered}`

Their point of intersection is given by (-3/2,0).