Key Features and Transformations of Functions

What kind of Function is this?

• Linear

• Absolute Value

• Quadratic

• Exponential

• None of the above

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

What kind of function is this?

• Linear

• Absolute Value

• Quadratic

• Exponential

• None of the above

Which equation represents this graph.

• f(x)=(x - 4)² - 3

• f(x)=-(x - 4)² + 3

• f(x)=(x - 4)² + 3

• f(x)=-(x + 4)² + 3

Tags

CCSS.HSF-IF.C.7A

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

The graph of a quadratic function f is shown and the vertex is labeled with its coordinates.  If g(x) = f(x - 1) + 2, what is the minimum value of g?

* The minimum value of g is ​ (a)   because the minimum value of f is ​ (b)   and the graph of g is shifted ​ (c)   from the graph of f by ​ ​ (d)   .​

• 6

• 4

• up

• 2

• 1

• 3

• 5

• down

• left

• right

The graph of f(x) = x² was transformed to create the graph of g(x) = f(x) – 9. Which statement about the graphs is true?

• The graph of g is a reflection of the graph of f across the x-axis.

• The vertex of the graph of g is 9 units to the right of the vertex of the graph of f.

• The graph of g is a reflection of the graph of f across the y-axis.

• The y-intercept of the graph of g is 9 units below the y-intercept of the graph of f.

The graph of a transformed squaring function is shown below. Which equation and description best describes the graph? Select the equation ​ (a)   and description ​ (b)  

• neither even nor odd function

• even function

• odd function

Tags

CCSS.HSF.BF.B.3

The graph of f(x) = x² was translated 4.5 units to the left to create the graph of function g. Which function represents g?

• g(x) = (x - 4.5)²

• g(x) = (x + 4.5)²

• g(x) = x² - 4.5

• g(x) = x² + 4.5

Determine the transformation in each function as it relates to the parent function f(x) = x² . Match each graph to the correct description.

• 
• 
• 
• 

• left

• right

• down

• up

• reflection