1.6 Checkpoints

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

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 blue function is the original function f(x) = x³. Which of the following is the correct equation for the red function, g(x)?

• $g\left(x\right)=x^3+1$

• $g\left(x\right)=x^3-1$

• $g\left(x\right)=\left(x-1\right)^3$

• $g\left(x\right)=\left(x+1\right)^3$

Tags

CCSS.HSF.BF.B.3

Identify the transformation from the graph of  $f\left(x\right)=\sin\left(x\right)$  to the graph of $g(x)=-\sin(x+5)$  

• shifted up five units

  reflection in x-axis

• shifted down five units

  reflection in x-axis

• shifted left 5 units

  reflection x-axis

• shifted right 5 units

  reflection x-axis

Tags

CCSS.HSF-IF.C.7E

Describe the transformation from dotted to solid.

• f(x + 5) + 3
• f(x +3) + 5
• f(x - 5) + 3
• f(x - 3) + 5

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.C.7

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

• Reflection over y-axis; Right 3; Up 1
• Right 3; Up 1
• Reflection over x-axis; Left 3; Up 1
• Reflection of x-axis; Right 3; Up 1

Tags

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.4

CCSS.HSG.CO.A.5

CCSS.HSG.CO.B.6

• A).
• B).
• C).
• D.)

Tags

CCSS.HSF-IF.C.7B

Which parent function matches the graph?

• y = |x|
• y = ∛(x)
• y = x²
• y = a⋅b^x

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

CCSS.HSF.IF.A.1

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

g(x)=f(x-4)
Describe the transformation to f(x) that results in g(x).

• f(x) has been translated to the right 4.
• f(x) has been translated to the left 4.

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2