sec math ii sage review functions assessment id: …sec math ii sage review functionssec math ii...

Sec Math II SAGE Review Functions

Sec Math II SAGE Review Functions Assessment ID: ib.327127

Generated On April 29, 2015, 12:07 PM PDT Illuminate Itembank™

1 Which of the following statements are true regarding the graph of ƒ(x) = x – 2 – 1? Select three thatapply.

A. The graph has a vertex located at (–2, –1).

B. The graph has a y–intercept located at (0, 1).

C. The graph has a y–intercept located at (0, 3).

D. The graph has an x–intercept located at (1, 0).

E. The graph has an x–intercept located at (3, 0).

2 If (f + g)(x) = 7x2 – 11x + 3, which of these could be f(x) and g(x)? Select three that apply.

A. f(x) = 3x2 – 6x – 4;g(x) = 4x2 – 5x + 1

B. f(x) = 7x + 3;g(x) = 7x2 – 18x

C. f(x) = –x3 + x2 + 3;g(x) = x3 + 6x2 – 11x

D. f(x) = 2x2 – 2x + 1;g(x) = 5x2 – 9x + 2

E. f(x) = x3 + 7x2 – 2x;g(x) = –9x + 3

F. f(x) = –8x + 1;g(x) = 7x2 – 3x + 3

3 A function is shown in the graph below.

Which of the following intervals are part of the domain of the function? Select three that apply.

A. –4 ≤ x ≤ 3

B. –4 < x < –3

C. –3 < x < –2

D. 1 ≤ x ≤ 3

E. 3 < x < 4


Directions: Answer the following question(s).

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4 Russell was given a list of functions and needed to identify the domain for each function. Hisanswers are in the table below.

For which functions did Russell correctly identify the domain? Select three that apply.

A. ƒ(x) = x2 – 3x – 4

B. ƒ(x) = √ x + 2

C. ƒ(x) = x – 3

D. ƒ(x) = 4x + 1

E. ƒ(x) = 3x




5 Which of the following graphs show a function of the form ƒ(x) = (x – c)2 + 3 for some real numberc? Select two that apply.

A.

B.

C.

D.

E.




6 Which of the following functions have the same y–intercept as the function below? Select three thatapply.

ƒ(x) = x2 – 7x + 12

A. ƒ(x) = (x – 3)(x – 4)

B. ƒ(x) = (x – 2)(x – 5)

C. ƒ(x) = x2 – 7x + 6

D. ƒ(x) = x2 – 8x + 12

E. ƒ(x) = (x – 1)2 + 12

F. ƒ(x) = (x – 2)2 + 8

7 Which of the following graphs shows a function of the form ƒ(x) = x – c for some real number c? Select two that apply.

A.

B.

C.

D.




8Which of the following piecewise graphs are given by y =

x

2 + 1 on the interval 4 < x < 6? Select two

that apply.

A.

B.

C.

D.

E.




9 During math class, the teacher wrote the equations below on the board.

x2 + y2 = 9y = x3 + 1x – y = 12y2 = x – 5

y = 1

x + 2

The teacher then told the class to only graph the equations that are functions. Which of thoseequations will the class need to graph? Select three that apply.

A. x2 + y2 = 9

B. y = x3 + 1

C. x – y = 12

D. y2 = x – 5

E.y =

1

x + 2

10 For which of the following intervals is the average rate of change of the function shown below equalto –1? Select two that apply.

A. 0 ≤ x ≤ 1

B. 0 ≤ x ≤ 3

C. 2 ≤ x ≤ 3

D. 2 ≤ x ≤ 4

E. 3 ≤ x ≤ 5

F. 4 ≤ x ≤ 5




11 A function is shown on the coordinate plane below.

Over which interval(s) is the function increasing? Select two that apply.

A. 2 < x < 3

B. 0 < x < 2

C. –1 < x < 0

D. –3 < x < –1

E. –4 < x < –3




12 Which of the following graphs shows a function with a domain of 2 ≤ x < 5? Select two that apply.

A.

B.

C.

D.

E.




13 Which of the following graphs shows a function whose domain is the interval [1, ∞)? Select two thatapply.

A.

B.

C.

D.

E.




14 The graph below shows a relationship between x and y. On which of the following intervals is thegraph increasing? Select two that apply.

A. 0 < x < 1

B. 1 < x < 2

C. 2 < x < 3

D. 3 < x < 4

E. 4 < x < 5

15

Which of the following equations will generate the graph above?

A. (x – 2)2 = (x + 2)2 + y

B. (x – 4)2 = y

C. (x + 4)2 = y

D. (x – 2)(x + 2) = y




16 Michelle kicks a soccer ball up into the air from the ground. The graph represents the height of theball, in feet, as a function of time, in seconds.

Select all of the values that are in the domain of the function represented by the graph.

A. –5 seconds

B. 0 seconds

C. 2.5 seconds

D. 6 seconds

E. 10 seconds

17 The function ƒ(x) is represented by ƒ(x) = x + 2. The graph of the function g(x) is graphed below.

In which of the following intervals are both functions increasing?

A. –∞ < x < 4

B. –∞ < x < ∞C. 4 < x < ∞D. 1 < x < 7




18

In which of the following intervals is the graph decreasing?

A. –2 < x < 2

B. 0 < x < 3

C. –2 < x < 0

D. 2 < x < 4

19 Let f(x) = 3x2.

Part A:Write an expression that represents the inverse of the function f(x).

f–1(x) =

Part B:Explain how you determined your answer.




20

Select the equation that represents the graph above.

A. y = √ x + 4 – 2

B. y = √ x – 4

C. y = √ x – 4 + 2

D. y = √ x + 4 + 2

21 On the coordinate grid below, draw the graph ƒ(x) = 1 – x + 2 .

22 Identify the domain and range of g x = 4 x−3A. D: x ≥ 3 ; R: y ≥ 0B. D: x ≥ 0 ; R: y ≥ 3

C. D: x ≥ −3 ; R: y ≥ 0D. D: x ≤ 3 ; R: y ≤ 0




23 In 1999, first-class postage for items that weighed up to one ounce was $0.33. Each additional ounce (orfraction of an ounce) cost $0.22 as shown in the graph below.

What is the domain of the "postage" function, shown in the graph above?

A. All real numbers, x, such that x > 0

B. All integers, x, such that x > 0

C. All integers

D. All real numbers

24 What is the domain of the function shown on the graph below?

A. {–7, –4, –3, –2, 1, 4, 5, 6, 7, 8}

B. {–7, –4, –3, 5, 7}

C. {–2, 1, 4, 5, 7}

D. {–2, 1, 4, 6, 8}




25 What is the domain of the function shown on the graph below?

A. all real numbers

B. all real numbers less than 4

C. all real numbers less than or equal to 4

D. all real numbers not equal to 2




26 Which BEST represents the graph of y = 3x2 – 3x?

A.

B.

C.

D.

27 Which quadratic function, when graphed, has x–intercepts of –10 and 6?

A. y = (1 – 10x)(6x + 1)

B. y = (x – 10)(x + 6)

C. y = (10x – 6)(6x + 10)

D. y = (x + 10)(2x – 12)




28Which BEST represents the graph of y =

1

4x2 – 4 ?

A.

B.

C.

D.




29Which is the graph of y = –

1

2(x – 3)2 – 1?

A.

B.

C.

D.

30 Which statement below can ONLY be true if the functions, ƒ(x) and g(x), are inverses of each other?

A.f–1(x) =

1

f(x)and g–1(x) =

1

g(x)

B. ƒ(g(x)) = x and g(ƒ(x)) = x

C. ƒ(ƒ(x)) = x and g(g(x)) = x

D. ƒ(g(x)) = g(ƒ(x))




31 Each of the four graphs below represents a function. Which function has an inverse that is also afunction?

A.

B.

C.

D.

32 If ƒ(x) = x2 – x and g(x) = –x + 5, what is ƒ(g(4) + 3) ?

A. 3

B. 8

C. 12

D. 16




33 Determine the range of the function whose graph is shown below:

A. {y | y ≥ 4}

B. {y | y ≤ 4}

C. {y | 0 ≤ y ≤ 4}

D. {y | –4 ≤ y ≤ 0}

34 If the graph of a quadratic function ƒ(x) = ax2 + bx + c intersects the x–axis at two points, which ofthe following statements below is true?

A. b2 – 4ac > 0

B. b2 – 4ac < 0

C. b2 – 4ac ≤ 0

D. b2 – 4ac = 0

35 Jamal used factoring to find the zeros of the equation 3x2 + 4x – 1 = 0. He concluded that since thispolynomial cannot be factored the graph does not intersect the x-axis. Is Jamal correct?

A. Yes. Jamal is correct that this quadratic cannot befactored and when that is the case its graph doesnot intersect the x-axis.

B. No. Jamal is correct that this quadratic cannot befactored, but when that is the case its graphintersects the x-axis at the vertex of the parabola.

C. No. Jamal is correct that this quadratic cannot befactored, but when that is the case there may stillbe real zeros which can be found using quadraticformula.

D. No. Jamal's reasing is sound, but he is wrongbecause this quadratic can be factored into(3x + 1)(x + 1), so it will intersect the x-axis twice.

36 Find the coordinates of the vertex for the graph of ƒ(x) = –x2 + 2x + 3.

A. (–1 , 0)

B. (1 , 4)

C. (1 , 6)

D. (2 , 3)




37Find a quadratic function in the form ƒ(x) = ax2 + bx + c where x =

1

4 is the axis of symmetry and the

y–intercept is (0 , –5).

A. ƒ(x) = 2x2 – x – 5

B. ƒ(x) = 2x2 + x – 5

C. ƒ(x) = 4x2 – x – 5

D. ƒ(x) = 4x2 – 5x + 1

38 If ƒ(x) = x2 + 1 and g(x) = 5x – 3, what is ƒ(g(x))?

A. 5x2 + 2

B. 25x2 + 10

C. 25x2 – 30x + 9

D. 25x2 – 30x + 10

39 Which set of numbers represents the RANGE in the following graph?

A. {–2, –1, 1, 2, 3}

B. {–3, –2, –1, 0, 1, 2, 3}

C. {0, 1, 2, 3}

D. {–3, –2, –1, 0, 2, 5}




40

What is the equation of the function shown above?

A.y = (x – 1

1

2) 2

– 3

B.y = (x – 1

1

2) 2

+ 3

C.y = –(x – 1

1

2) 2

+ 3

D.y = –(x – 1

1

2) 2

– 3



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sec math ii sage review functions assessment id: …sec math ii sage review functionssec math ii...

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