Question

Help quick

1. Graph f(x)=2x+1 and g(x)=−x+7 on the same coordinate plane.

What is the solution to the equation f(x)=g(x) ?

2. Let ​ f(x)=x+2f(x)=x+2 ​ and ​ g(x)=2x+1 ​ .

Graph the functions on the same coordinate plane.


What are the solutions to the equation f(x)=g(x) ?



Enter your answers in the boxes.

x =
or x =

Answer 1

1 & 0

Explanation:

Answer 2

1.You have two ways for solving this.
First, you could use a graphing utility or calculator to graph both functions on the same plane, and given that the functions do not have a
`y` coordinate, the solution of
`f(x)=g(x)` will be the
`x` coordinate in which the tow graphs intercept (cross each other) as you can see in the picture (1).
The other way is equating the two equations and solve for x:
We know that
`f(x)=2x+1` and
`g(x)=-x+7`, so
`f(x)=g(x)` is equivalent to
`2x+1=-x+7`. The only thing left is solving the equation for x:

`2x+1=-x+7`

`3x=6`

`x=2`
As you can see, both ways gives us the same answer: the solution to the equation
`f(x)=g(x)` is
`x=2`.

2. For this one we can repeat the exact same procedures as before:
Graph the functions on the same plane using a graph calculator or graphing utility, and identify the
`x` coordinate in which the two graphs intercept as you can see in the picture (2), or you we can also equate both equations, and solve for
`x`:

`x+2=2x+1`

`x=1`
And just like before, both ways gives us the same answer: the solution to the equation
`f(x)=g(x)` is
`x=1`

So, the answer that you should enter in your boxes are: 2 in the first, and 1 in the second one.