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Quiz 1: Elementary functions

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Question 1

Find the gradient and the y-intercept of the straight line through the points (4,3) and (7,5).

a)
gradient 32 and y-intercept 13.
   b)
gradient 23 and y-intercept 13.
c)
gradient 3 2 and y-intercept -1 2.
   d)
gradient 2 3 and y-intercept -1 2.

 

Not correct. Choice (a) is false.
Your answer is correct.
m = 5--3-= 2 7- 4 3 .
therefore,y = 2 3x + b ⇒ 3 = 8 3 + b ⇒ b = 1 3.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.

Question 2

Find the equation of the straight line through (1,1) and (8,-2).

a)
3x - 7y = 10
   b)
3x + 7y = -10
c)
3x + 7y = 10
   d)
3x - 7y = -10

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Your answer is correct.
Gradient = -37, y-intercept=170.
Not correct. Choice (d) is false.

Question 3

The equation of the line through (1,1) and (3,4) is

a)
3y - 2x - 1 = 0
   b)
2y - 3x - 1 = 0
c)
3x - 2y - 1 = 0
   d)
2y + 3x - 1 = 0

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Your answer is correct.
m = 4--1-= 3 3- 1 2
3 3 1 therefore,y = 2x + b ⇒ 1 = 2 + b ⇒ b = 2
therefore,y = 3x - 1⇒ 2y = 3x - 1 ⇒ 3x- 2y- 1 = 0. 2 2
Not correct. Choice (d) is false.

Question 4

Which of the following is the graph of y = -2(x + 1)2 + 4?

a)
PIC
   b)
PIC
c)
PIC
   d)
PIC

 

Not correct. Choice (a) is false.
Not correct. This is the graph of 2(x + 1)2 + 4.
Not correct. Choice (b) is false.
Not correct. This is the graph of -2(x - 1)2 + 4.
Your answer is correct.
Not correct. Choice (d) is false.
Not correct. This is the graph of (x + 1)2 + 4.

Question 5

Which of the following expressions is equivalent to -3x2 - 3x + 7?

a)
-(3x + 32)2 + 52
   b)
-3(x -12)2 + 314
c)
-3(x + 12)2 + 314
   d)
-3(x + 1)2 + 10
e)
None of the above

 

Not correct. Choice (a) is false.
Incorrect answer.
Not correct. Choice (b) is false.
Incorrect answer.
Your answer is correct.
Correct answer.
- 3x2 - 3x+ 7 = - 3(x2 + x)+ 7 1 1 = - 3(x2 + x +( )2 - ( )2)+ 7 1 23 2 = - 3(x+- )2 + -+ 7 21 431 = - 3(x+- )2 + -- 2 4
Not correct. Choice (d) is false.
Incorrect answer.
Not correct. Choice (e) is false.
Incorrect answer. One of the above responses is the correct answer.

Question 6

PIC Which of the following functions describes the above graph?

a)
y = -(x - 1)2 + 2
   b)
y = 2x(2 - x)
c)
y = -2(x + 1)2 + 2
   d)
y = 2(x - 1)2 + 2
e)
None of the above.

 

Not correct. Choice (a) is false.
Incorrect answer. The given graph is “taller“ or “skinnier“ than the graph of y = -(x- 1)2 + 2. You can see that this answer is incorrect by plotting some points.
Your answer is correct.
Correct. This expression is equal to y = -2(x - 1)2 + 2.
Not correct. Choice (c) is false.
Incorrect answer. This function has its turning point at x=-1
Not correct. Choice (d) is false.
Incorrect answer. The graph of this function will point upwards.
Not correct. Choice (e) is false.
Incorrect answer. Oe of the above responses is the correct answer.

Question 7

Simplify e2xe5x2 .

a)
e7x2
  b)
3 e10x
c)
x(2+5x) e
  d)
2x 5x2 e + e

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Your answer is correct.
2x 5x2 2x+5x2 x(2+5x) e e = e = e .
Not correct. Choice (d) is false.

Question 8

Simplify ( 3) ln ab- c2 .

a)
lna + ln3b - ln2c
   b)
lna + 3lnb - 2lnc
c)
3lnab - 2lnc
   d)
3lnab - ln2c

 

Not correct. Choice (a) is false.
Your answer is correct.
( 3) ln ab- = lnab3 - lnc2 c2 = lna+ lnb3 - 2 lnc = lna+ 3 ln b- 2lnc.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.

Question 9

Which of the following is the graph of y = -e(x-2) + 1?

a)
PIC
   b)
PIC
c)
PIC
   d)
PIC
e)
None of the above

 

Your answer is correct.
Not correct. Choice (b) is false.
Incorrect answer.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
Not correct. Choice (e) is false.
Incorrect answer. One of the above responses is the correct answer.

Question 10

Which of the following graohs represents the function y = (x + 2)-1 + π?

a)
PIC
   b)
PIC
c)
PIC
   d)
PIC

 

Not correct. Choice (a) is false.
Incorrect answer. You need to move this graph up π units. π is approximately equal to 3.14
Not correct. Choice (b) is false.
Incorrect answer. Hint: (x + 2)-1 = 1 x+2.
Your answer is correct.
Not correct. Choice (d) is false.
Incorrect answer. The given function has a vertical aymptote at x + 2 = 0, i.e. x = -2. Hint: (x + 2)-1 = -1- x+2
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