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1 vote
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 =

2 Answers

2 votes

Answer:

1 & 0

Explanation:

Help quick 1. Graph f(x)=2x+1 and g(x)=−x+7 on the same coordinate plane. What is-example-1
User Nick Ball
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8.0k points
3 votes
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.
Help quick 1. Graph f(x)=2x+1 and g(x)=−x+7 on the same coordinate plane. What is-example-1
Help quick 1. Graph f(x)=2x+1 and g(x)=−x+7 on the same coordinate plane. What is-example-2
User Flauntster
by
8.1k points