Shifting Functions Review

The function $g\left(x\right)$  is the function  $f\left(x\right)=2\left(x-1\right)^2+3$  shifted 3 units right and 2 units down.  Which of the following is the equation for  $g\left(x\right)?$  

•  $g\left(x\right)=2\left(x+2\right)^2+1$  

•  $g\left(x\right)=2\left(x-3\right)^2-2$  

•  $g\left(x\right)=2\left(x+3\right)^2-2$  

•  $g\left(x\right)=2\left(x-4\right)^2+1$  

How do the functions  $y=f\left(x+2\right)$  and  $y=f\left(x-3\right)$  differ?

• f(x + 2) is 2 units right of f(x - 3)

• f(x + 2) is 5 units left of f(x - 3)

• f(x + 2) is 5 units to the right of f(x - 3)

• f(x + 2) is 1 unit to the left of f(x - 3)

Which statement below describes what happens to the graph of  $y=a\left(x-h\right)^2+k$  when the value of  $a$  is changed from   $-1$  to  $-3?$  

• the graph translates 2 units down

• the graph translates 2 units right

• the graph widens (shrinks vertically)

• the graph narrows (stretches vertically)

Which of the following is the graph of $y=\left(x-5\right)^2+3$ ? 

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Tags

CCSS.HSF-IF.C.7A

Which statement describes what happens to the graph of  $y=a\left(x-h\right)^2+k$  when the value of  $h$  is changed from  $2$  to  $-1?$  

• the graph translates 3 units down

• the graph translates 3 units right

• the graph translates 3 units up

• the graph translates 3 units left

• the graph stretches vertically by a factor of 3

The function  $g\left(x\right)$  can be described as  $g\left(x\right)=2f\left(x+1\right)-5.$  Which best describes the relationship between  $g\left(x\right)$  and  $f\left(x\right)?$  

• g(x) is f(x) shifted 1 unit right, stretched vertically by a factor of 2, and shifted 5 units down.

• g(x) is f(x) shifted 1 unit left, stretched vertically by a factor of 2, and shifted 5 units down.

• g(x) is f(x) shifted 1 unit left, compressed vertically by a factor of 2, and shifted 5 units up.

• g(x) is f(x) shifted 1 unit right, stretched vertically by a factor of 2, and shifted 5 units up.

• $g\left(x\right)=f\left(x-3\right)-2$

• $g\left(x\right)=f\left(x+3\right)-2$

• $g\left(x\right)=f\left(x-3\right)+2$

• $g\left(x\right)=f\left(x+3\right)+2$

• Exponential function

• Square root function

• Absolute value function

• Linear function

Which statement describes what happens to the graph of  $y=a\left(x-h\right)^2+k$  when the value of  $k$  is changed from  $-1$  to  $4?$  

• the graph translates 3 units up

• the graph translates 3 units right

• the graph translates 5 units right

• the graph translates 5 units up