Study

Question 1

Why is 3ln(1/2) < 2ln(1/2)?

Answer 1

3ln(1/2) = 3ln(2^-1)=-3ln(2)
and 2ln(1/2)=2ln(2^-1)=-2ln(2).

-3ln(2) < -2ln(2)

Question 2

If a function has a curved top what is the interval?

Answer 2

Closed

Question 3

An interval is closed when asked to find where a function is increasing/decreasing when

Answer 3

The top is rounded

Question 4

Why is sin^-1(sin 4π/3) = -π/3?

Answer 4

sin(π-θ)= sin, so:

sin(π-4π/3)=sin(-π/3) which is in the range of sin^-1.

Question 5

sin(π-θ)= sin, so:

sin(π-4π/3)=sin(-π/3) which is in the range of sin^-1.

Answer 5

sin^-1(sin 4π/3) = -π/3

Question 6

What does it mean to find a domain where f is one-to-one?

Answer 6

Find where it is defined

Question 7

Simplify with exponent rules:

√a √b/ √ab

Answer 7

a^1/6 / b^1/12

Question 8

Find domain:

h(x)=1/ ^4√x^2 -5x

Answer 8

(-∞, 0) U (5, ∞) because x(x-5)>0 is equal to x<0 and x>5

Question 9

Find domain:

f(x)= √16-x^4 / x^2 -1

Answer 9

[-2,-1)U(-1,1)U(1,2] because x cannot equal +-1 and x<=+-2 which equals -2<=x<=2

Question 10

If a function is always decreasing, never zero, and f(-2)=1 and f(1)=2, what is the graph?

Answer 10

A piecewise function.

Question 11

What does cos(-x) equal?

Answer 11

cos(x)

Question 12

What does sin(-x) equal?

Answer 12

-sin(x)

Question 13

Equals -sin(x)

Answer 13

sin(-x)

Question 14

Simplify:

2x(4-x)^-1/2 - 3√4-x = 0

Answer 14

x=12/5 because you put (4-x)^-1/2 under 2x and ass 3√4-x to right side. Then solve for x.

Question 15

How is this absolute value function solved?:

3|x-4|=10

Answer 15

|x-4|=10/3

Then x-4=10/3 and x-4=-10/3

Question 16

Simplify:

3x^3/2•y^3 / x^2•y^-1/2

Answer 16

9y^7 / x because you multiply all exponents by 2 first. Then any negative exponents are flipped and solve.

Question 17

How is this simplified?

√200 - √32

Answer 17

Split into one non-squarable and squarable:

√2 • √100 - √2 • √16

√2 • 10 - √2 • 4

6√2

Question 18

Evaluate:

y/x - x/y / 1/y - 1/x

Answer 18

• (y+x) because (y+x)(y-x) / x-y =

- (y+x)(x-y) / x-y

Question 19

How is this evaluated?:

16^-3/4

Answer 19

Equals 1/(16^1/4)^3

1/2^3

1/8

Question 20

How do you prove:

√x^2 = x

Answer 20

√(-2)^2 = -2 so false

Question 21

How do you prove:

a^2+b^2=c^2

Answer 21

(1)^2+(2)^2=(3)^2 so false

Question 22

How do you prove:

√xy

Answer 22

Equals √x•√y

x^1/2 • y^1/2

(xy)^1/2 = √xy so true

Question 23

If the half-life is 4 days, what is the mass after 16 days?

Answer 23

(1/2)^t/4 where t is days and 4 is half-life

Question 24

Difference between rational and algebraic equations

Answer 24

Rational has polynomial on numerator AND denominator

Question 25

Rational has polynomial on

Answer 25

numerator AND denominator

Question 26

Evaluate this log: log(5)(200/8)

Answer 26

log(5)(25) so 2

Question 27

Solve for x: 2^x = 5^3x+7

Answer 27

x=7ln(5) / ln(2) - 3ln(5) because you take exponent out and distribute.

Question 28

If you have domain and need range, what is done?

Answer 28

Test values of domain for highest and lowest values of range.

Question 29

Test values of domain for highest and lowest values of range.

Answer 29

If you have domain and need range

Question 30

Why is cos^-1(-1)= π?

Answer 30

Because cosine hits -1 every π

Question 31

Because cosine hits -1 every π, this means the inverse would be.

Answer 31

cos^-1(-1)= π

Question 32

What is the domain of ln(x)<0?

Answer 32

3^ln(x)

Question 33

Definition of one-to-one funct

Answer 33

Function that never takes on the same value twice

Question 34

Function that never takes on the same value twice

Answer 34

One-to-one

Question 35

Find exponential function given two points: | 1,12) and (3,108

Answer 35

12=C(b^1)=Cb 108=C(b^3)=Cb^3 C=12/b (solve for C) 108= 12/b•(b^3)=12b^2 (plug in C in second) b=3 (solve for b) C=12/3 = 4 so, y=4(3)^x

Question 36

How is number e defined?

Answer 36

The value so that the slope of the tangent like to y=e^x at (0,1) is exactly 1.

Question 37

The value so that the slope of the tangent like to y=e^x at (0,1) is exactly 1.

Answer 37

e

Question 38

How is this divided?: 9^3 / 3^-8

Answer 38

Flip 1/9^3 / 1/3^8 1/9^3 • 3^8 3^8 / 9^3 3^8 / (3^2)^3 3^8 / 3^6 3^2

Question 39

The graph of y=1/3x + b is shrunk by a factor of

Answer 39

3 not 1/3

Question 40

Is f(s+t)=f(s)+f(t)?

Answer 40

No because (f+f)(x)=f(x)+f(x)

Question 41

Suppose g is an even function and let h=f o g. Is h always an even function?

Answer 41

Yes because if g = x every time being even, then so is f o g

Question 42

Volume of sphere

Answer 42

4/3πr^3

Question 43

4/3πr^3

Answer 43

Volume of sphere

Question 44

Graph the function y=|x^2 -9|

Answer 44

Same as regular x^2 graph but x’s from -3 to 3 are reflected over x-axis

Question 45

Equation for two families if functions if one family’s is y=5x+b and the other’s is y=m(x-5)+1.

Answer 45

5x+b=m(x-1)+1 and solve

Question 46

If a box has dimensions 18in. by 30in and gets equal squares of side x at each corner folded up, express the new volume as a function of x.

Answer 46

V=lwh so, V=(30-2x)(18-2x)x

Question 47

If the sides of a rectangle box, (not the bases), are the height (h) and the length (2w), and also the width (w), what is the cost of all the sides?

Answer 47

2[2(wh) + 2(2wh)] since the area for 2 sides is 2(wh) total, and the other two sides is 2(2wh) total.

Question 48

If the material for the base of a rectangular box costs $8 per square meter, what is the total cost if w is the width and 2w is the length?

Answer 48

A=lw so, (2w)(w)=2w^2 Multiply 8 by this number for the cost: 8(2w^2)

Question 49

In general, if f(x)=g(x) when x cannot equal a, then

Answer 49

``` lim f(x) = lim g(x) x—>a x—>a ```

Question 50

Substituting limit points directly into functions only works for

Answer 50

Polynomials and rationals

Question 51

Only works for polynomials and rationals

Answer 51

Substituting limit point directly into a function

Question 52

Domain of tan function

Answer 52

nπ/2

Question 53

nπ/2

Answer 53

Domain of tangent function

Question 54

How is cot graphed?

Answer 54

Tangent but backwards

Question 55

Tangent but backwards on graph

Answer 55

Cot

Question 56

Domain and range of cos^-1

Answer 56

R: [0, π] D: [-1,1]

Question 57

Domain and range of sin^-1

Answer 57

D: [-1,1] R: [-2π, 2π]

Question 58

When reflection about a y value, what is done?

Answer 58

Add negative at base and add twice the y-value

Question 59

Add negative at base and add twice the y-value

Answer 59

When reflection about a y value

Question 60

When reflecting about x-values what is done?

Answer 60

Add negative at x and add twice the x-value

Question 61

Add negative at x and add twice the x-value

Answer 61

When reflecting about x-values

Question 62

Order of transformations

Answer 62

``` H-shift H-stretch/shrink Reflect y-axis Vert-stretch/shrink Reflect x-axis Vert-shift ```

Question 63

To find x-values of log function what is done?

Answer 63

Set praenthesis equal to 0, 1, and the base and solve

Question 64

Set praenthesis equal to 0, 1, and the base and solve

Answer 64

To find x-values of log function