Horizontal and Vertical Transformations of Functions

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

g(x) = 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.

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

• x² + 2
• x² - 2
• (x + 2)²
• (x - 2)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(x)=x³+1
• g(x)=x³-1
• g(x)=(x-1)³
• g(x)=(x+1)³

Tags

CCSS.HSF.BF.B.3

Let f(x) = |x + 1|. Which function would have a graph that is 5 units down of the graph of f?

• g(x) = |x + 1| + 5

• g(x) = |x + 1| - 5

• g(x) = |x + 6|

• g(x) = |x - 4|

Tags

CCSS.HSF.BF.B.3

Let f(x) = x² + 8. Which function would have a graph that is 2 units down of the graph of f?

• g(x) = x² + 6

• g(x) = x² + 10

• g(x) = (x - 2)² + 6

• g(x) = (x +2)² + 6

Tags

CCSS.HSF.BF.B.3

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

Tags

CCSS.HSF.BF.B.3

Let f(x) = |x + 1|. Which function would have a graph that is 5 units left of the graph of f?

• g(x) = |x + 1| + 5

• g(x) = |x + 1| - 5

• g(x) = |x + 6|

• g(x) = |x - 4|

Tags

CCSS.HSF.BF.B.3

Let f(x) = x² + 8. Which function would have a graph that is 5 units right of the graph of f?

• g(x) = x² + 13

• g(x) = x² + 3

• g(x) = (x - 5)² + 8

• g(x) = (x +5)² + 8

Tags

CCSS.HSF.BF.B.3

Let f(x) = (x + 2)² + 3. Which function would have a graph that is 2 units right and 3 units up of the graph of f?

• g(x) = x² + 6

• g(x) = (x + 4)² + 6

• g(x) = x²

• g(x) = (x + 4)²

Tags

CCSS.HSF.BF.B.3

• $𝑦=𝑓(𝑥+5)+3$

• $𝑦=𝑓(𝑥−5)−3$

• $𝑦=𝑓(𝑥+5)−3$

• $𝑦=𝑓(𝑥−5)+3$

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7