The University of Sydney
Faculty of Economics and Business  
MathQuiz  

Logarithmic and Square Root Graphs - Quiz 3   Last unanswered question  Question  Next unanswered question

Question 1 lion

Which of the following graphs represents        -----
y = √ x+ 1?
a) PIC   b) PIC
c) PIC   d) PIC

 

Not correct. Choice (a) is false.
Try again, this is  y = lnx .
Your answer is correct.
This is      √-----
y =  x + 1.
Not correct. Choice (c) is false.
Try again, this is   y = ex.
Not correct. Choice (d) is false.
Try again, this is      √--
y =  x .
Remember   √ -
  0 = 0.
Question 2 lion

Which of the following graphs represents   y = lnx+ 1 ?
a) PIC   b) PIC
c) PIC   d) PIC

 

Not correct. Choice (a) is false.
Try again, this is   y = ex.
Not correct. Choice (b) is false.
Try again, this is   y = ln x.
Not correct. Choice (c) is false.
Try again, this       √--
y =  x .
Your answer is correct.
This is   y = ln(x+ 1).
Question 3 lion

What is the value of   f(x) = 2lnx- 3    at   x = 1?
a) f(1) = 5 .    b) f (1) = - 1.
c) f(1) = - 3 .    d) f (1)    is undefined.

 

Not correct. Choice (a) is false.
Try again, remember   ln 1 = 0.
Not correct. Choice (b) is false.
Try again, remember   ln 1 = 0 .
Your answer is correct.
Since   ln1 = 0    we have   2ln 1- 3 = - 3.
Not correct. Choice (d) is false.
Try again, remember   ln 1 = 0.
Question 4 lion

What is the value of        √-----
f(x) =  5 - x    at  x = 1?
a) f(1) = 2.    b) f(1) = - 2.
c) f(1) = 4.    d) The function is undefined at x = 1.

 

Your answer is correct.
Since  √-----  √ -
 5 - 1 =  4 = 2.
Not correct. Choice (b) is false.
Try again, watch the negative signs.
Not correct. Choice (c) is false.
Try again, you have omitted the square root.
Not correct. Choice (d) is false.
The domain of this function is (- infty,5)  since we cannot take the
square root of a negative number. Hence the function is defined at  x = 1.
Question 5 lion

Consider the graph below.

PIC
Which function is best described by this graph?
a) f (x) = 3+ lnx .
 1    b) f(x) = 3- ln x.
 1
c) f (x) = √x-.
 1    d) f (x) = √x-+ 2 .
 1

 

Your answer is correct.
This is the right shape for y = a+ b lnx  and it passes through  (1,3)
so it is  y = 3 + lnx    and this is the only choice of this type.
Not correct. Choice (b) is false.
Try again, this is the wrong shape for  y = a- blnx.
Not correct. Choice (c) is false.
Try again,  f (1) = 3
 1    in this function.
Not correct. Choice (d) is false.
Try again, the function does not pass through  (0,2).