Transformations and Key Features

Multiple Choice

Which equation describes the transformation of shifting f(x)=x² two units right?

• x² + 2

• x² - 2

• (x + 2)²

• (x - 2)²

Multiple Choice

Given f(x) = (x-3)² + 5.  What transformations took place from the original function f(x)?

• Left 3 and up 5
• Right 3 and down 5
• Left 3 and down 5
• Right 3 and up 5

Multiple Choice

. 
If the blue is f(x)=x^2, then the red must be

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

Multiple Choice

What do we call the highest or lowest point of a quadratic?

• parabola
• vertex
• graph
• point

Multiple Choice

Identify the y-intercept

• (0, -3)

• (0, 1)

• (0, 3)

• (2, 1)

Multiple Choice

What is the domain of the graph?

• All real numbers
• To infinity and beyond
• y ≥ 0
• x ≥ 0

Multiple Choice

What is the range of the graph?

• All real numbers
• To infinity and beyond
• y ≥ 0
• x ≥ 0

Multiple Choice

What is the domain of the graph?

• All real numbers
• To infinity and beyond
• y ≥ -1
• x ≥ 0

Multiple Choice

What is the range of the graph?

• All real numbers
• To infinity and beyond
• y ≥ -1
• x ≥ 0

Multiple Choice

What variable represents the domain?

• x

• y

• d

• r

Multiple Choice

What variable represents the range?

• x

• y

• d

• r

Multiple Choice

What is the Domain of this exponential function?

• y=1

• x=0

• All Real Numbers

• x>0

Multiple Choice

What is the Range of this function?

• y > 0

• x> 0

• All Real Numbers

• y > 1

Multiple Choice

What is the range of the exponential function?

• all real numbers

• y > -1

• y < -1

• x > -1

Multiple Choice

What is the range of the exponential function?

• all real numbers

• y > 3

• y < 3

• x > 3

Multiple Choice

What is the domain of the exponential function?

• all real numbers

• y > 3

• y < 3

• x > 3

Multiple Choice

Which equation describes the transformation of shifting f(x)=x² two units right?

• x² + 2
• x² - 2
• (x + 2)²
• (x - 2)²

Multiple Choice

Identify the transformation from the graph of f(x)=x² to the graph g(x)= -(x+5)² 

• 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

Multiple Choice

Given f(x) = (x-3)² + 5.  What transformations took place from the original function f(x)?

• Left 3 and up 5
• Right 3 and down 5
• Left 3 and down 5
• Right 3 and up 5

Multiple Choice

Describe the transformation

$$f\left(x\right)+3$$  

• 3 Units Up

• 3 Units Down

• 3 Units Left

• 3 Units Right

Multiple Choice

f(x) = 5x² + 2

• Stretch of 5
  Up 2
• Shrink of 5
  Up 2
• Stretch of 5
  Down 2
• Shrink of 5
  Down 2

Multiple Choice

• g(x)=2x²
• g(x)=0.5x²
• g(x)=x²+2
• g(x)=(x+2)²

Multiple Choice

. 
If the blue is f(x)=x^2, the red must be

• g(x)=(x+3)²
• g(x)=(x-3)²
• g(x)=x²+3
• g(x)=x²-2

Multiple Choice

What are the following transformations?
- f(x+2)

• reflection over the y axis and 2 units to the right
• reflection over the x axis and 2 units right
• reflection over the y axis and 2 units left
• reflection over the x axis and 2 units left

Multiple Choice

Which equation describes the transformation of shifting f(x)=x³ four units down?

• x³+ 4
• x³- 4
• (x - 4)³
• (x + 4)³

Multiple Choice

Which equation describes the transformation of shifting f(x)=x³ seven units up?

• x³+7
• x³-7
• (x-7)³
• (x+7)³

Multiple Choice

Which equation describes the transformation of shifting f(x)=x³ three units left?

• x³ + 3
• x³ - 3
• (x + 3)³
• (x - 3)³

Multiple Choice

Identify the transformation from the graph of f(x)=2^x to the graph g(x)=2^x-3

• shifted up three units
• shifted down three units
• shifted left three units
• shifted right four units

Multiple Choice

Which describes how the graph of $$g\left(x\right)=x^2+2$$ is related to the function $$f\left(x\right)=x^2$$

• translation of $$f\left(x\right)=x^2$$ up 2 units.

• translation of $$f\left(x\right)=x^2$$ down 2 units.

• translation of $$f\left(x\right)=x^2$$ left 2 units.

• translation of $$f\left(x\right)=x^2$$ right 2 units.

Multiple Choice

Which describes how the graph of $$g\left(x\right)=\left(x-1\right)^2$$ is related to the function $$f\left(x\right)=x^2$$

• translation of $$f\left(x\right)=x^2$$ up 1 unit.

• translation of $$f\left(x\right)=x^2$$ down 1 unit.

• translation of $$f\left(x\right)=x^2$$ left 1 unit.

• translation of $$f\left(x\right)=x^2$$ right 1 units.

Multiple Choice

Which describes how the graph of $$g\left(x\right)=x^2-8$$ is related to the function $$f\left(x\right)=x^2$$

• translation of $$f\left(x\right)=x^2$$ up 8 units.

• translation of $$f\left(x\right)=x^2$$ down 8 units.

• translation of $$f\left(x\right)=x^2$$ left 8 units.

• translation of $$f\left(x\right)=x^2$$ right 8 units.

Multiple Choice

Which describes how the graph of $$g\left(x\right)=7x^2$$ is related to the function $$f\left(x\right)=x^2$$

• dilation of $$f\left(x\right)=x^2$$ stretched vertically.

• dilation of $$f\left(x\right)=x^2$$ compressed vertically.

• dilation of $$f\left(x\right)=x^2$$ stretched horizontally.

• dilation of $$f\left(x\right)=x^2$$ compressed horizontally.

Match

Match the following in the vertex form of the quadratic equation.

$$f\left(x\right)=a\left(x-h\right)^2+k$$

• $$f\left(x\right)$$

• a

• h

• k

• x

y

reflection, vertical stretch, or compression

horizontal translation

vertical translation

x-value

• y

• reflection, vertical stretch, or compression

• horizontal translation

• vertical translation

• x-value

Multiple Choice

If the blue is f(x)=x^2, then the red must be

• g(x) = x² - 5

• g(x) = x² + 5

• g(x) = (x - 5)²

• g(x) = (x + 5)²

Multiple Choice

f(x) is transformed so that it maps onto g(x). Which equation would correctly represent g(x)

• g(x) = x² - 3

• g(x) = x² + 3

• g(x) = (x - 3)²

• g(x) = (x + 3)²

Multiple Choice

The vertex of the quadratic function f(x) in the picture is (-4, 5).

If g(x) = f(x) translated LEFT 2 units , what is the vertex of g(x)?

• (-2, 5)
• (-6, 5)
• (-4, 3)
• (-4, 7)

Multiple Choice

The vertex of the quadratic function f(x) in the picture (2, -2).

If g(x) = f(x) translated DOWN 4 units , what is the vertex of g(x)?

• (2, -6)

• (2, 2)

• (-2, -2)

• (6, -2)

Multiple Choice

Compare the function y = 0.3x² to the parent function y = x²

• Wider

  (Vert. Compress)

• Narrower

  (Vert. Stretch)

Multiple Choice

Compare the function y = 5x² to the parent function y = x²

• Wider

  (Vert. Compress)

• Narrower

  (Vert. Stretch)

Multiple Choice

Match the equation to its description.

• Reflected over x and stretched by 3
• Stretched by 3
• Reflected over x
• Reflected over x and down 3

Multiple Choice

Match the equation to its description.

• Reflected over x, right 2 and up 1
• Reflected over x, left 2 and up 1
• Reflected over x, right 2 and down 1
• Reflected over x, left 2 and down 1

Multiple Choice

Describe the transformation of y = 3(x - 3)² + 3

• Narrow, Right, Up
• Narrow, Left, Down
• Wide, Right, Up
• Wide, Left, Down