Question

Which of the following options has (have) the correct combination of the function and its graph?

• A. $y=-3(x-\frac{1}{2}),x\le 2$
  
• B. $y=3$
  
• C. $y=2x-3,x>-4$
  
• D. $y=-5x$
  

Answer 1

Answer: (A), (C), (D)

The correct options are
A $y=-3(x-\frac{1}{2}),x\le 2$

C $y=2x-3,x>-4$

D $y=-5x$


$y=-3(x-\frac{1}{2})$
$\Rightarrow y=-3x+\frac{3}{2}$
It is parallel to $y=-3x$ and passes through $(0,1.5)$


Since $x\le 2,$ we can ignore the graph in the right side of $x=2$



$y=3$ is parallel to $x-$axis and $3$ units above $x-$axis.


$y=2x-3$
It is parallel to $y=2x$ and passes through $(0,-3)$


Since $x>-4,$ we can ignore the graph in the left side of $x=-4,$ including $x=-4$


$y=-5x$