Basic Graphing Help Involving Functions and Solutions

Question

Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4(–x) and y = 2(x + 3) intersect are the solutions of the equation 4(–x( = 2(x + 3) 

Part B: Make tables to find the solution to 4(–x) = (2x + 3) Take the integer values of x between −3 and 3. 

Part C: How can you solve the equation 4(–x( = 2(x + 3) graphically?

Answer 1

Transitive property of equality:

If a=b and b=c then a=c

 

we have y = 4(-x) and y= 2(x+3)

as simultaneous equations.  By the TPOE

above, this means:

4(-x) = 2(x+3)

 

-4x = 2x + 6

-6x = 6

x = -1

These lines intersect at the point (-1, 4)

 

On Part B you changed the equation:

x    | 4(-x)  | 2(x+3)

----|--------|------------

-3  |   12    |    0

-2  |    8     |   2

-1  |   4      |   4  

0   |   0      |   6

1   |  -4      |   8

2   |  -8      |   10

3   |  -12    |   12

 

As can be seen both graphs contain

the point (-1, 4) which is the solution

of the system.

 

To solve graphically using the table just made,

plot any two points for (x, -4x) and draw that line.

Then plot any two points from (x, 2(x+3)) and

draw that line.  The crossing point should be at

(-1, 4)