Transformations Vertical and Horizontal Translation Review

From the line y = x , which line shifted down 3 units 

• y = 3x

• y = x + 3

• y = -3x

• y = x - 3

Which transformation transforms the graph of
f(x) = x² to the graph of g(x) = (x + 4)²?

• a vertical translation 4 units up

• a vertical translation 4 units down

• a horizontal translation 4 units to the left

• a horizontal translation 4 units to the right

Quadratic functions q and w are graphed on the same coordinate grid.  The vertex of the graph of q is 18 units below the vertex of the graph of w.  Which pair of functions could have been used to create the graphs of q and w?

• q(x) = 18x² and w(x) = x²

• q(x) = x² + 18 and w(x) = x²

• q(x) = -18x² and w(x) = x²

• q(x) = x² - 18 and w(x) = x²

Jordan sketched the graph of the function f(x) = x.  Then he made the following transformations to create the function h:  He shifted the function 3 units down, 4 units to the left and made it less steep by a factor of 1/2.  Which function shows the transformations that Jordan made?

• h(x) = 1/2f(x - 3) + 4

• h(x) = 1/2f(x + 4) - 3

• h(x) = 1/2f(x + 3) - 4

• h(x) = f(x + 4) - 3

Given the equation for this parabola:
 y=-(x-4)²-3,
does this parabola have a maximum or minimum value?

• Maximum

• Minimum

Tags

CCSS.HSF-IF.C.7A

In the equation f(x)=5(x+3)²-10 what effect does the 5 do when compared to the parent function?

• Vertical stretch by a factor of 5

• Vertical shrink/compress by a factor of 5

• Reflect over x-axis

• Vertical shift up 5 units

Describe the transformation of y = f(x) for the new function
 y = f(x) - 5

• The graph of y = f(x) was shifted to the right 5 units. 

• The graph of y = f(x) was shifted to the left 5 units. 

• The graph of y = f(x) was shifted up 5 units. 

• The graph of y = f(x) was shifted down 5 units.

Tags

CCSS.HSF.BF.B.3

Which transformation will occur if f(x) = x is replaced with f(x) + 2?

• Translation left 2 units

• Translation right 2 units

• Vertical translation up by 2 units.

• Reflection across the x-axis.

How did the equation shift from the parent function? y = f(x - 4)

• Shift right by 4

• Shift left by 4

• Horizontal Stretch by 4

• Vertical Stretch by 4

• Shift down by 4

Describe the transformation to y = f(x) if it is replaced with y= (x - 1) - 5.

• f(x) has been translated to the left one and down five.

• f(x) has been translated to the right one and down five.

• f(x) has been translated to the left one and up five.

• f(x) has been translated to the right one and up five.