Test 5

Question 1

How do you find the inverse?

Answer 1

1. Replace f(x) by y
2. Switch x and y
3. Solve for y
   Replace y with f-1(x)

Question 2

Domain and range of f and f-1

Answer 2

Domain of f= real zero
Range of f= domain of f-1
Domain of f-1= real zero
Range if f-1= domain of f

Question 3

What is the graph of f(x)=e^x

Answer 3

Y=0 xintercept is 1

Question 4

F(x) +k

Answer 4

Shifts up k units

Question 5

F(x)-k

Answer 5

Shift down k units

Question 6

F(x+p)

Answer 6

Shift left p units

Question 7

F(x-p)

Answer 7

Right p units

Question 8

-F(x)

Answer 8

Reflect graph about x axis

Question 9

F(-x)

Answer 9

Reflect graph about y axis

Question 10

Graph of G(x)=log2^x

Answer 10

X=0 yintercept is 1

Question 11

Properties or logarithms

Answer 11

1. Log a 1= 0 a^0=1
2. Log a a = 1 a^1=a
3. Log a a^r= r a^r= a^r

Question 12

3 rules of logarithms

Answer 12

I. Log a M +Log a N= Log a(M*N)
II. Log a M- Log a N= Log a(M/N)
III. rLog a M= Log a M^r

Question 13

How do you know if a function is a one to one?

Answer 13

Ordered pairs: no repeating 2nd component ex (2,4) (3,7)
Graph: does it pass the horizontal line test?

Question 14

How do you draw the inverse of a graph?

Answer 14

Switch the points. (A,b) (b,a)

Question 15

Logarithmic equations case 1: when the equation has a constant

Answer 15

Log a X = C 》a^c=x

Question 16

Case 2: when the equation has logarithms only

Answer 16

Log a U= Log a V 》U=V