Graphical Transformations

Which equation below is a quadratic function translated left 4 units?

• y = x² + 4
• y = (x + 4)²
• y = (x - 4)²
• y = 4x²

Tags

CCSS.HSF.BF.B.3

Which equation below is a quadratic function translated up 5 units?

• y = x² + 5
• y = (x + 5)²
• y = 5x²
• y = -x² - 5

Tags

CCSS.HSF.BF.B.3

How would the following graph differ from the graph of f(x)?

 $f\left(x-2\right)-4$  

• horizontal shift to the right 2 and vertical shift up 4

• horizontal shift to the right 2 and vertical shift down 4

• horizontal shift to the left 2 and vertical shift up 2

• horizontal shift to the left 2 and vertical shift down 2

Tags

CCSS.HSF.BF.B.3

The green line represents the function

 $y\ =\ x^2$ 
What function is represented by the blue line?

•  $y\ =\ -x^2\ -\ 3$  

•  $y\ =\ -x^2\ +\ 3$  

•  $y\ =\ -\left(x+3\right)^2$  

•  $y\ =\ -\left(x-3\right)^2$  

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.C.7

CCSS.HSA.REI.D.11

CCSS.HSF.BF.B.3

CCSS.HSF.IF.C.7

Upon which line is the green line reflected to produce the blue line?

• The x-axis

• The y-axis

• The line y = x

Tags

CCSS.HSF.BF.B.3

The green line is represented by the function

 $y\ =\ x^3\ +\ 3$  
On the last question, you found that to get from the green line to the blue, we reflected about the line y = x. 

Using this information, what is the equation of the blue line?

•  $y\ =\ ^3\sqrt{x\ +\ 3}$  

•  $y\ =\ ^3\sqrt{x\ -\ 3}$  

•  $y\ =\ ^3\sqrt{x\ }\ +\ 3$  

•  $y\ =\ ^3\sqrt{x}\ -\ 3$  

Answer explanation

Remember, when you reflect about the line y = x, you've found the INVERSE. 

Tags

CCSS.HSF.BF.B.3

The green line, again, represents

 $y\ =\ x^3\ +\ 3$  
Which equation represents the orange line? (Notice: Reflection about the X-axis)

•  $y\ =\ x^3\ -\ 3$  

•  $y\ =\ -x^3\ +\ 3$  

•  $y\ =\ -\left(x^3\ -\ 3\right)$  

•  $y\ =\ -\left(x^3\ +\ 3\right)$  

Answer explanation

Remember, reflection about the x-axis transforms  $f\left(x\right)\ to\ -f\left(x\right).$  

Tags

CCSS.HSF.BF.B.3

Once more, the green line represents

 $y\ =\ x^3\ +\ 3$  
Which equation represents the purple line? (Notice: reflection about the Y-axis.)

•  $y\ =\ -x^3\ +\ 3$  

•  $y\ =\ -x^{3\ }-\ 3$  

•  $y\ =\ -\left(x^3\ +\ 3\right)$  

•  $y\ =\ ^3\sqrt{x\ +\ 3}$  

Answer explanation

Remember, changing  $f\left(x\right)\ to\ f\left(-x\right)$  will reflect the graph around the Y-axis.

Tags

CCSS.HSF.BF.B.3

The orange line represents the function

 $y\ =\ x^2$  
What is one possible equation for the green line?

•  $y\ =\ 3x^2$  

•  $y\ =\ -x^2$  

•  $y\ =\ \frac{1}{5}x^2$  

•  $y\ =\ x^2\ +\ 3$  

Tags

CCSS.HSA.CED.A.2

CCSS.HSF.BF.A.1

Again, the orange line represents

 $y\ =\ x^2$  
What is one possible equation for the blue line?

•  $y\ =\ 5x^2$  

•  $y\ =\ x^{2\ }-\ 3$  

•  $y\ =\ -\frac{1}{2}x^2$  

•  $y\ =\ -6x^2$  

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11