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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) = 2?

 

 Jan 27, 2021
 #1
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Line 1: Slope = 2. Y-Intercept = 3. Equation: y = 2x + 3. When y = 2, x = -1/2.

Line 2: Slope = -1. Y-Intercept = -3. Equation: y = -x - 3. When y = 2, x = -5.

Line 3: Given. When y = 2, x = 1.

Line 4: Given. When y = 2, x = 1.

Line 5: Slope = 2. Y-Intercept = -3. Equation: y = 2x - 3. When y = 2, x = 5/2.

 

-1/2 + -5 + 1 + 1 + 5/2 = -1

 

Hope this helps!

 

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 Jan 27, 2021
 #2
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f(x)  =  2    means  that  y   = 2

 

Only two points on this graph intersect  this line  .....   (1,2)  and  ( 2.5, 2)

 

So...the sum of the x coordinates  =    1 + 2.5 =   3.5

 

 

cool cool cool

 Jan 27, 2021

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