Parent Functions Transformations Increasing Decreasing Domain and Range

Describe the transformations, asymptote, domain, and range for the following function: f(x)=-3(2)^{(x-4)}+6

• Transformation: Vertically stretched factor 3, translated right 4 and down 6. 
  Horizontal Asymptote at y = - 6 
  Domain: (-∞,∞)   Range: (-∞,6)

• Transformation: Reflection over x-axis, vertically stretched factor 3, translated right 4 and up 6. 
  Horizontal Asymptote at y = 6 
  Domain: (-∞,∞)   Range: (-∞,6)

• Transformation: Reflection over x-axis, vertically stretched factor 1/3, translated Left 4 and up 6. 
  Horizontal Asymptote at y = 6 
  Domain: (-∞,∞)   Range: (6,-∞)

• Transformation: Reflection over x-axis, vertically stretched factor 1/3, translated Left 4 and Down 6. 
  Horizontal Asymptote at y =6
  Domain: (-∞,∞)   Range: (6,-∞)

Using the following absolute value f(x)=|x-4|-6 check all of the true statements.

• The vertex of the absolute value function is (4,-6)

• 
  The Range of the absolute value function is
  [−6,∞)

• The Domain of the absolute value function is (-inf,INF)

• An increasing interval of the absolute value is

  (4, inf)

Using the following absolute value f(x) =|x-4|-6 find where the graph is increasing and decreasing. Check all that apply

Use the graph of g(x) = 2|x|+1 determine all of the true statements.

• The vertex is a minimum at the point (0,1)

• The Vertex is a maximum at the point (0,1)

Given the function h(x) = |2x-4| - 7 check all of the statements that are false.

• The vertex is ( 2, -7)

• The vertex is (4,-7)

• The x- intercepts of the absolute value function is x=-1.5 and x= 5.5

• [−7,∞)

  The range of the function is [

Given the parent function f(x) =|x|, what transformations have taken place to get the new function f(x) = -2|x+4|+6. Check all that apply.

• The function has translations left four and up six

• The function has translations right four and up six

• The function is reflected over the x-axis

• The function has a vertical stretch of two

• The function has vertical compression of two

Given the parent function f(x ) =|x| , what transformations have taken place to get the new function f(x)= |2x|- 6. Check all that apply

• The absolute value has a vertical translation of down 6

• The absolute value has a horizontal compression of 1/2

• The absolute value has a horizontal stretch of 2

• The absolute value has a reflection about the x-axis.

Identify where the function is increasing and where it is decreasing.

• increasing (-1, ∞) and decreasing (-∞,-1)

• increasing (-∞, -1) and decreasing (-1, ∞)

• increasing (-∞,∞) and decreasing nowhere

• increasing (-1, -4) and decreasing (-3, 1)

Identify the function's domain and range.

• domain (-∞,∞) and range (-∞,∞)

• domain (-∞, ∞) and range (-4,∞)

• domain (-∞,∞) and range [-4,∞)

• domain [-3, 1] and range [-4,∞)

Which comparison is correct?

• The blue graph has a smaller minimum than the red graph.

• The red graph has a smaller minimum than the blue graph.

• The red and blue graph have the same minimum value.

• The red graph has a larger maximum than the blue graph.