+0  
 
0
150
1
avatar

The complete graph of \(y=f(x)\), which consists of five line segments, is shown in red below. (On this graph, the distance between grid lines is  \(1\).)

 

What is the sum of the \(x\)-coordinates of all points where \(f(x) = 1.8\)?

 

Guest May 12, 2018
 #1
avatar+91078 
+1

If we let  f(x)  = y, we are looking for the the x coordinates of the form  ( x , 1.8)

 

The first segment which contains  a points like this   is the segment from  (0, 0)  to (1,2)

The slope of the line containing this segment  is  [ 2 - 0 ] / [1 - 0]    = 2

And the equation of this line is   y  = 2x

So...when y  = 1.8, we have

1.8  = 2 x     divide both sides by 2

.9  = x

 

So....the first point is  (.9, 1.8)

 

 

The next segment containing the y valu of 1.8  is  the segment from (1,2) to (2,1)

The slope of the line containing this segment is  (1 - 2)  /( 2 -1)  = -1/1  = -1

And the equation of this line is

y  = -(x -1) + 2

y  = -x + 3

And when y  = 1.8, we have

 

1.8  = -x + 3  subtract 3 from both sides

-1.2  = -x

1.2   = x

 

So.....the second point  is  ( 1.2, 1.8)

 

The last point where  y  = 1.8  is on the segment from (2,1)  to (3,3)

The sloe of the line containing this point is   (3 - 1)  /( 3 - 2)  =   2/ 1   = 2

And the equation of the line  containing this segment is

y =2 ( x -3) + 3

y = 2x  - 6 + 3

y = 2x  - 3

And when y  = 1.8, we have

1.8 = 2x  - 3    add 3 to both sides

4.8  = 2x   divide both sides by 2

2.4  = x

 

So....the last point is  ( 2.4, 1.8)

 

So....the sum of the x coordinates where  f(x)  = 1.8  is   .9 + 1.2 + 2.4  = 4.5

 

 

 

cool cool cool

CPhill  May 12, 2018

26 Online Users

avatar
avatar
avatar
avatar
avatar
avatar
avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.