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The graphs of two linear functions, f(x) and g(x), are shown here on one set of axes:

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+808

The graphs of two linear functions, f(x) and g(x), are shown here on one set of axes:

Each small box in the grid is 1 unit by 1 unit.  Evaluate f(g(1)) * g(f(1)).

ASAP answers would be greatly appreciated! Thanks so much!

AnonymousConfusedGuy  Dec 15, 2017

#1
+6616
+1

Evaluate     f( g(1) ) * g( f(1) )

First we need to find  g(1)  and  f(1) .

On the orange line, when  x = 1 ,  y = -2 .  So  when  x = 1,  g(x) = 2 .  g(1) = -2

On the blue line, when  x = 1 ,  y = 1.5 .  So  when  x = 1 ,  f(x) = 1.5 .  f(1) = 1.5

So........

f( g(1) ) * g( f(1) )   =   f( -2 ) * g( 1.5 )

Now we need to find  f( -2 )  and  g( 1.5 ) .

On the blue line, when  x = -2 ,  y = 3 .  So  when  x = -2 ,  f(x) = 3 .  f(-2) = 3

On the orange line, when  x = 1.5 ,  y = -1 .  So when  x = 1.5 ,  g(x) = -1 .  g(1.5) = -1

So......

f( g(1) ) * g( f(1) )   =   f( -2 ) * g( 1.5 )   =   3  *  -1  =   -3

hectictar  Dec 15, 2017
Sort:

#1
+6616
+1

Evaluate     f( g(1) ) * g( f(1) )

First we need to find  g(1)  and  f(1) .

On the orange line, when  x = 1 ,  y = -2 .  So  when  x = 1,  g(x) = 2 .  g(1) = -2

On the blue line, when  x = 1 ,  y = 1.5 .  So  when  x = 1 ,  f(x) = 1.5 .  f(1) = 1.5

So........

f( g(1) ) * g( f(1) )   =   f( -2 ) * g( 1.5 )

Now we need to find  f( -2 )  and  g( 1.5 ) .

On the blue line, when  x = -2 ,  y = 3 .  So  when  x = -2 ,  f(x) = 3 .  f(-2) = 3

On the orange line, when  x = 1.5 ,  y = -1 .  So when  x = 1.5 ,  g(x) = -1 .  g(1.5) = -1

So......

f( g(1) ) * g( f(1) )   =   f( -2 ) * g( 1.5 )   =   3  *  -1  =   -3

hectictar  Dec 15, 2017
#2
+808
+1

Thanks :D

AnonymousConfusedGuy  Dec 15, 2017

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