Pure Math 30 - Conics Diagnostic PRE-TEST
1. The horizontal translation for the function y 2 f (4 x 8) 1 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 y x 2 x 6 is shown. Which transformation will not affect the x-intercepts for this y 10 graph? a) y f ( x)
1 c) y f ( x) 2
( ) ( )
b) y f ( x) 2
-10 -5
5 -5
10 x
d) y 2 f ( x)
-10
( )
( )
( )
( )
( )
3. Which pair of transformations produces different images, depending on the order in which the transformations are applied? a) horizontal translation and vertical compression c) horizontal expansion and a horizontal reflection b) horizontal translation and horizontal compression d) horizontal compression and a vertical expansion
Numerical Response #1 The point A(7, 1) exists on the graph of y f (x) . When the function is transformed to a new function, y 2 f [3( x 4)] 5.5 , the value of the x-coordinate, to the nearest hundredth is:___________
1 4. The function defined by p( x) ( x 2)( x 4)( x 6) has x-intercepts of -6, -2, 4. If x x , then the 2 zeros will be:
a) -8, -4, 2
b) -6, -2, 4
c) -8, 4, 12
d) -2, -1, 3
5. For any given function, y f ( x) , if the y is replaced with 3y, then the resulting transformation is a: a) vertical stretch by a factor of 3 c) horizontal stretch by a factor of 3 b) vertical stretch by a factor of
1 3 1 3
d) horizontal stretch by a factor of
6. The graph of y f (x) is shown. The range of the function is f ( x) 11. If the function f (x) is transformed to a new function g ( x) f ( x 2) 3 , then the range of g (x) will be: a) g ( x) 14 c) g ( x) 9 b) g ( x) 9 d) g ( x) 14
x y
y f ( x)
11
7. The vertical asymptotes of the reciprocal of the function f ( x) x 2 2 x 3 are: a) x 1 and x 3 b) y 1 and y 3 c) y 1 and y 3 d) x 1 and x 3
8. Which equation represents the image of the graph of y 2 x 5 after a horizontal stretch by a factor 1 of and a reflection in the x-axis? 2
Numerical Response #2
1 Given the graph of y f (x) , the y-intercept of y , to the nearest hundredth, is: 3 f ( x)
-5
y f ( x)
5 x
9. The graph of y f (x) is shown to the right. If the graphs of y same grid, the point that will be invariant for all three graphs is:
1 and y f 1 ( x) are sketched on f ( x)
y
a) point R c) point P
b) point S d) point Q
x
y 6 5 4 3 2 1 -4 -3 -2 -1 -1 -2 1 2 3 4 x
10. The graph of y f ( x) is shown. The domain of y f 1 ( x) is: a) x 2 c) 2 x 2 b) x 0 d) x R
11. If the function y f ( x 1) 2 is horizontally stretched by a factor of and then translated 3 units to the left, then the new equation is: a) y f (2 x 5) 2 b) y f (2 x 2) 2 c) y f (2 x 4) 2 d) y f (2 x 7) 2
Numerical Response #3
The point below is horizontally stretched by a factor of of a, to the nearest tenth is:________
4 about the line x 3 , to the point (a, b). The value 5
y 4 3 2 1
(4,3)
-3
-2
-1 -1 -2
12. A mapping rule is defined by ( x, y) (2 x 1, 4 y 3) . The mapping rule describes the transformations that have occurred. Which transformation is an incorrect description? a) there is a reflection in the y-axis c) there is a vertical stretch by a factor of 4 b) there is a horizontal translation 1 unit right d) there is a vertical translation 3 units up
13. Given f ( x) x3 9 , the equation for the function that is reflected in the line y x is: a) f ( x) 3 x 9 b) f ( x) 3 x 9 c) f ( x)
1 x 9
3
d) f ( x)
1 x9
Written Response Show all work for full marks. 1. Given the graph of y f (x) , i) give the mapping rule used to transform each point (1 mark each) ii) sketch the graph of each transformation (2 marks each)
1 a) y 4 f ( x) 1 2
*Use a different colour for each. y
15
10
- 15
- 10
-5 -5
10
15
b) y
1 f [3( x 2)] 6 2
- 10
- 15
y 10
2. Given y f (x) , sketch the graph of y **Label the characteristics CAREFULLY.
1 . (3 marks) f ( x)
- 10 -5 5 10
-5
- 10
3. Describe the transformations on y f (x) that have taken place to produce y 4 f (2 x 12) 5 . Use proper terminology. (3 marks)
