Unit 4 Optional Review: Function Analysis (Bartels M3H)

1

f(x)=x^2 has been transformed to h(x). The graph of h(x) is shown. Which of the following is true about h(x)?
I. h(x) is reflected over the x-axis
II. h(x)=-1(x-4)^{2}+4
III. The is domain is (-∞, ∞)
IV: h(x) is negative on (4, ∞)

1

Which of the following value of “b” would cause a horizontal stretch to the graph of parent quadratic function?

1

Which of the following value of “b” would cause a horizontal compression to the graph of parent quadratic function?

1

Which of the following value of “a” would cause a vertical compression to the graph of parent quadratic function?

1

Which of the following value of “a” would cause a vertical stretch to the graph of parent quadratic function?

1

The function f(x)=x^2 has been transformed to g(x) such that g(x)= 3(-2x-6)+2. Which of the following is not true about the graph of gx when compared to f(x)?

1

All of the following functions have a vertical shift in the graph except:

1

Consider the piecewise function described by the following equation. What is f(-3)?

1

Consider the piecewise function described by the following equation. What is f(5)?

1

Which of the graphs has odd symmetry?

1

Which of the graphs has even symmetry?

1

Which of the following functions have an absolute minimum? Select all that apply.

1

Which of the following functions have an absolute maximum? Select all that apply.

1

Which of the following piecewise function matches the graph below?

1

Which of the following are true about the graph below? Select all that apply.

1

A absolute minimum is also an relative minimum.

1

A piecewise function only contains one function but has a restricted domain.

2

Graph the function on the coordinate plane provided. Mark your points and indicate open versus closed circles clearly.


Domain:_______ 
Range:_______ 

1

Given the graph of y=f(x), list all of the transformations given by y= -2f(x+2)-1.
Transformation:

1

Given the graph of y=f(x), list all of the transformations given by y= -2f(x+2)-1. Then, sketch the graph of the transformed function. Make sure to mark at least 4 exact points. 
New points:
(-5,1) becomes _______  
(-3,-4) becomes _______ 
(0,0) becomes_______
(3,-4) becomes_______ 
(5,1) becomes _______ 

13

Identify all of the following key features for the graph given.

If it doesn’t exist, state none.
Relative maximum(s):_______ 
Relative minimum(s):_______ 
Absolute maximum(s):   _______ 
Absolute minimum(s):_______ 
Decreasing interval(s):   _______ 
Increasing interval(s):_______ 
Constant(s):_______ and _______ 
Negative Interval(s):_______ 
Positive Interval(s):_______ and _______ 
End Behavior:
as x→-8, y→_______ 
as x→∞, y→_______ 

10

Identify all of the following key features for the graph given.

If it doesn’t exist, state none.
Relative maximum(s):_______ 
Relative minimum(s):_______ 
Absolute maximum(s):   _______ 
Absolute minimum(s):_______ 
Decreasing interval(s):   _______ 
Increasing interval(s):_______ and _______ 
Constant(s):_______ 
End Behavior:
as x→-∞, y→_______ 
as x→∞, y→_______ 

Unit 4 Optional Review: Function Analysis (Bartels M3H)

f(x)=x^2 has been transformed to h(x). The graph of h(x) is shown. Which of the following is true about h(x)?I. h(x) is reflected over the x-axisII. h(x)=-1(x-4)^{2}+4III. The is domain is (-∞, ∞)IV: h(x) is negative on (4, ∞)

Which of the following value of “b” would cause a horizontal stretch to the graph of parent quadratic function?

Which of the following value of “b” would cause a horizontal compression to the graph of parent quadratic function?

Which of the following value of “a” would cause a vertical compression to the graph of parent quadratic function?

Which of the following value of “a” would cause a vertical stretch to the graph of parent quadratic function?

The function f(x)=x^2 has been transformed to g(x) such that g(x)= 3(-2x-6)+2. Which of the following is not true about the graph of gx when compared to f(x)?

All of the following functions have a vertical shift in the graph except:

Consider the piecewise function described by the following equation. What is f(-3)?

Consider the piecewise function described by the following equation. What is f(5)?

Which of the graphs has odd symmetry?

Which of the graphs has even symmetry?

Which of the following functions have an absolute minimum? Select all that apply.

Which of the following functions have an absolute maximum? Select all that apply.

Which of the following piecewise function matches the graph below?

Which of the following are true about the graph below? Select all that apply.

A absolute minimum is also an relative minimum.

A piecewise function only contains one function but has a restricted domain.

Given the graph of y=f(x), list all of the transformations given by y= -2f(x+2)-1. Transformation:

f(x)=x^2 has been transformed to h(x). The graph of h(x) is shown. Which of the following is true about h(x)?I. h(x) is reflected over the x-axisII. h(x)=-1(x-4)^{2}+4III. The is domain is (-∞, ∞)IV: h(x) is negative on (4, ∞)

Which of the following value of “b” would cause a horizontal stretch to the graph of parent quadratic function?

Which of the following value of “b” would cause a horizontal compression to the graph of parent quadratic function?

Which of the following value of “a” would cause a vertical compression to the graph of parent quadratic function?

Which of the following value of “a” would cause a vertical stretch to the graph of parent quadratic function?

The function f(x)=x^2 has been transformed to g(x) such that g(x)= 3(-2x-6)+2. Which of the following is not true about the graph of gx when compared to f(x)?

All of the following functions have a vertical shift in the graph except:

Consider the piecewise function described by the following equation. What is f(-3)?

Consider the piecewise function described by the following equation. What is f(5)?

Which of the graphs has odd symmetry?

Which of the graphs has even symmetry?

Which of the following functions have an absolute minimum? Select all that apply.

Which of the following functions have an absolute maximum? Select all that apply.

Which of the following piecewise function matches the graph below?

Which of the following are true about the graph below? Select all that apply.

A absolute minimum is also an relative minimum.

A piecewise function only contains one function but has a restricted domain.

Given the graph of y=f(x), list all of the transformations given by y= -2f(x+2)-1. Transformation:

f(x)=x^2 has been transformed to h(x). The graph of h(x) is shown. Which of the following is true about h(x)?
I. h(x) is reflected over the x-axis
II. h(x)=-1(x-4)^{2}+4
III. The is domain is (-∞, ∞)
IV: h(x) is negative on (4, ∞)

Given the graph of y=f(x), list all of the transformations given by y= -2f(x+2)-1.
Transformation:

f(x)=x^2 has been transformed to h(x). The graph of h(x) is shown. Which of the following is true about h(x)?
I. h(x) is reflected over the x-axis
II. h(x)=-1(x-4)^{2}+4
III. The is domain is (-∞, ∞)
IV: h(x) is negative on (4, ∞)

Given the graph of y=f(x), list all of the transformations given by y= -2f(x+2)-1.
Transformation: