Topic 1 - Term Test 1

Question 1

1.3

What is the vertical asymptote of the tangent function?

Answer 1

x = pi/2 + kpi for k is an element of integers

Question 2

1.1

Distinguish between odd and even functions

Answer 2

Even is symmetric across y (-x, y)
Odd is symmetric across origin (-x,-y)

Question 3

1.3

What is the difference between
sin^-1(X) and (sinx)^-1

Answer 3

1st one is inverse and second one is reciprocal

Question 4

1.4
Inverses of basic trig functions

Answer 4

Arcsin
D = [-1,1]
R = [-pi/2, pi/2]

Arccos
D = [-1, 1]
R = [0, pi]

Arctan
D = (-inf, inf)
R = (-pi/2, pi/2)

Question 5

1.4

Solve sinx = 1/2 for x

Answer 5

Cannot use arcsin because question asks for ALL x that satisfy the equation

so it would be pi/6 + 2kpi and 5pi/6 + 2kpi because sin repeats every pi

Question 6

1.4

Given f(x) now find f-1(2)

Answer 6

Instaed of finding the inverse, just know that f-1(2) is the same as f(x) = 2 and find where this is true

Question 7

1.1

Domain of ln(x^2 -3x)

Answer 7

Whatever is in ln has to be greater than 0 and factoring out gives this

(x)(x-3)>0

Critical points are found setting equation equal to 0 and you get x = 0 and x = 3

Use sign chart and sub in values below 0, between 0 and 3, and above 3 and do teh sign analysis

Wherever the sign is positive is where the interval should include

Question 8

1.1

How to write absolute function as piecewise?

Answer 8

Use function statement if very simple.

But if a little more complex then set the equation equal to 0 and find critical point and how function behaves before and after critical point

Question 9

1.5

Domain of ln(ln(ln(x))))

Answer 9

ln(x) - x is greater than 0
for ln(lnx) - lnx > 0, raise both sides to the e and you get x>1
for ln(ln(x) you need lnx>1 thus raising to both sides equals e

Question 10

1.5
solve for x

2e^3x = 53^8x

Answer 10

take ln of both sides and you have product of 2 and e^3x, so ln 2 is a constant and ln(e^3x) is just 3x