Conics Pre Test

8/2/2019 Conics Pre Test

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Pure Math 30 - Conics Diagnostic PRE-TEST

1. The horizontal translation for the function 1)84(2 xfy is:

a) 2 units to the left b) 2 units to the right c) 8 units to the left d) 8 units to the right

2. The graph of 62 xxy is shown. Which transformation will not affect the x-intercepts for this

graph?

a) )( xfy b) 2)( xfy

c) )2

1( xfy d) )(2 xfy

3. Which pair of transformations produces different images, depending on the order in which the

transformations are applied?

a) horizontal translation and vertical compression b) horizontal translation and horizontal compressionc) horizontal expansion and a horizontal reflection d) horizontal compression and a vertical expansion

The point A(7, 1) exists on the graph of )(xfy . When the function is transformed to a new function,

2 [3( 4)] 5.5y f x , the value of thex-coordinate, to the nearest hundredth is:___________

4. The function defined by )6)(4)(2()( xxxxp hasx-intercepts of -6, -2, 4. If1

2

x x , then the

zeros will be:

a) -8, -4, 2 b) -6, -2, 4 c) -8, 4, 12 d) -2, -1, 3

Numerical Response #1

()


2/4

x

y

5. For any given function, ( )y f x , if they is replaced with 3y, then the resulting transformation is a:

a) vertical stretch by a factor of 3 b) vertical stretch by a factor of 13

c) horizontal stretch by a factor of 3 d) horizontal stretch by a factor of 13

6. The graph of )(xfy is shown. The range of the function is 11)( xf . If the function )(xf istransformed to a new function 3)2()( xfxg , then the range of )(xg will be:

a) 14)( xg b) 9)( xg

c) 9)( xg d) 14)( xg

7. The vertical asymptotes of the reciprocal of the function 32)( 2 xxxf are:

a) 3and1 xx b) 3and1 yy c) 3and1 yy d) 3and1 xx

8. Which equation represents the image of the graph of 52 xy after a horizontal stretch by a factor

of2

1and a reflection in thex-axis?

Given the graph of )(xfy , the y-intercept of1

3 ( )y

f x , to the nearest hundredth, is:

9. The graph of )(xfy is shown to the right. If the graphs of)(

1

xfy and )(

1xfy

are sketched on

same grid, the point that will be invariant for all three graphs is:

a) point R b) point Sc) point P d) point Q

( )y f x

x

y

11


x-5 5

y

5y


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x-3 -2 -1 1 2 3 4

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-1

1

2

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4

10. The graph of ( )y f x is shown. The domain of1( )y f x

is:

a) 2x b) 0x

c) 2 2x d) x R

11. If the function ( 1) 2y f x is horizontally stretched by a factor of and then translated 3 units to the

left, then the new equation is:

a) (2 5) 2y f x b) (2 2) 2y f x c) (2 4) 2y f x d) (2 7) 2y f x

The point below is horizontally stretched by a factor of4

5about the line 3x , to the point (a, b). The value

ofa, to the nearest tenth is:________

12. A mapping rule is defined by ( , ) ( 2 1,4 3)x y x y . The mapping rule describes the transformations

that have occurred. Which transformation is an incorrect description?

a) there is a reflection in they-axis b) there is a horizontal translation 1 unit right

c) there is a vertical stretch by a factor of 4 d) there is a vertical translation 3 units up

13. Given 3( ) 9f x x , the equation for the function that is reflected in the line y x is:

a) 3( ) 9f x x b) 3( ) 9f x x c)3

1( )

9f x

x

d)3

1( )

9f x

x


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y

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Written Response Show all work for full marks.

1. Given the graph of )(xfy ,

i) give the mapping rule used to transform each point (1 mark each)ii) sketch the graph of each transformation (2 marks each) *Use a different colour for each.

a)1

4 ( ) 12

y f x

b)1

[3( 2)] 62y f x

2. Given )(xfy , sketch the graph of)(

1

xfy . (3 marks)

**Label the characteristics CAREFULLY.

3. Describe the transformations on )(xfy that have taken place to produce 4 (2 12) 5y f x . Useproper terminology. (3 marks)

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Conics Pre Test