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The graph of y = f(x) is shown below. Assume the domain of f is [-4,4] and that the vertical spacing of grid lines is the same as the horizontal spacing of grid lines. 

size(150);real ticklen=3;real tickspace=2;real ticklength=0.1cm;real axisarrowsize=0.14cm;pen axispen=black+1.3bp;real vector...

Part (a): The points (a,4) and (b,-4) are on the graph of y = f\left( 2x \right). Find a and b. 

Part (b): Find the graph of y = f\left( 2x \right). Verify that your points from part (a) are on the graph. 

Part (c): The points (c,4) and (d,-4) are on the graph of y = f\left( 2x - 8 \right). Find c and d. 

Part (d): Find the graph of y = f\left( 2x - 8 \right). Be sure to verify that your points from part (c) are on the graph both algebraically and geometrically. 

Please include graphs in your answer! Thank you!

Guest Nov 16, 2014

Best Answer 

 #1
avatar+91507 
+5

If it makes you feel any better I struggled with this one - but I think it is right.  

 

Part a       y=f(2a)

 

f(-4)=4   but    f(2a)=-4    so   2a=-4     so   a=-2

 

f(4)=-4   but    f(2b)=4     so    2b=4      so    b=2

 

Part c        y=f(2a-8)

 

f(-4)=4  but    F(2c-8)=-4    so   2c-8=-4    so   2c=4    so    c=2

 

f(4)=-4  but  f(2d-8)=4  so  2d-8=4   so  2d=12     so d=6  but this is outside the domain so it does not exist

 

Melody  Nov 17, 2014
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1+0 Answers

 #1
avatar+91507 
+5
Best Answer

If it makes you feel any better I struggled with this one - but I think it is right.  

 

Part a       y=f(2a)

 

f(-4)=4   but    f(2a)=-4    so   2a=-4     so   a=-2

 

f(4)=-4   but    f(2b)=4     so    2b=4      so    b=2

 

Part c        y=f(2a-8)

 

f(-4)=4  but    F(2c-8)=-4    so   2c-8=-4    so   2c=4    so    c=2

 

f(4)=-4  but  f(2d-8)=4  so  2d-8=4   so  2d=12     so d=6  but this is outside the domain so it does not exist

 

Melody  Nov 17, 2014

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