Transformations
Compositions
Logs & Exponentials
Solving Equations
Rational Functions
Inverses
Miscellaneous
100
Write the equation that translates the absolute value function three units to the right.
|x-3|
100
Given: f(x)=3x+2 and g(x)=5x
What is the simplified composition g(f(x))?
15x+10
100
Expand the following:
log(a^2b^3c)
2log(a)+3log(b)+log(c)
100
Solve:
812x+1 * 243x =35
1/13
100
Factor the following:
x2-11x+30
(x-5)(x-6)
100
If f(x) has domain (2,7) and range (-4,9) - what would be the domain of f-1 ?
(-4,9)
100
If a function H gives a person's height off the ground in feet when skydiving at any time t. What would H inverse do?
H inverse would be able to take a person's height off the ground and give the time that they've been falling.
200
What transformations occurred on this parent?
y = -3(2x-9)2-8
Right 9
Horizontal shrink by 1/2
Vertical stretch by 3
Reflect Over x-axis
Down 8
200
Given f(x)=3x2 and g(x)=sqrt(3x+9)
Find f(g(x)) and state the domain.
f(g(x)) = 9x+27
D: [-3, inf)
200
Write a function for the situation:
A population of 18000 bees is decreasing by 3.8% every six years. Where p(t) is the population at t years.
p(t) = 18000(1-.038)t/6 or equivalently
p(t) = 18000(0.962)t/6
200
Solve for x. Give your solution as a decimal rounded to the nearest thousandth.
4 * 156x+9 - 5 = -3
-1.543
200
The end behavior for the rational given below is:
\frac{3x^2-27}{x^2+2x-3}
\lim_{x\rightarrow\infty}f(x)=3
\lim_{x\rightarrow-\infty}f(x)=3
200
Find the inverse function of:
y=3x-9
f^-1(y)=\frac{1}{3}y+3
200
What is the domain for:
3ln(x+2) / (x-2)
(-2,2) U (2,inf)
300
Write the equation that shows the exponential function reflected over both axes and shifted up four.
y = -e-x+4
300
Given: f(x) = log(x) and g(x)=5x-12
Find: g(f(1000))
3
300
What is log25(5)?
1/2
300
Solve: -9log(-x-10)=-36
-10010
300
Give the domain of the following rational. Describe points of discontinuity as holes or VAs
\frac{3x^2-27}{x^2+2x-3}
Hole at -3, VA at 1
(-\infty,-3)U(-3,1)U(1,\infty)
300
Find the inverse of
y=3(x-2)2 with original domain: [2,inf)
Domain of inverse?
Domain of inverse: [0,inf)
f^-1(y)=2+\sqrt(y/3)
300
What is the domain & range for:
y = 3ln(2x-8)+10
D: (4, inf)
R: (-inf, inf)
400
A horizontal shrink by 1/2 on the squaring function is equivalent to what other transformation on the squaring function?
Vertical stretch by 4.
400
Given: g(x)=ln(x) and f(x)=e2x+10
Find g(f(x)) and state the domain.
g(f(x)) = 2x+10
D: (-inf,inf) because e^(2x+10) has domain of all reals and range of (0,inf) which matches the domain of ln(x) perfectly!
400
How long does it take for 80% of a radioactive substance to decay if it's half life is 425 years?
Round your answer to the nearest thousandth.
986.819 years.
400
Solve: log(2x2+8) + log(4) = 3
11 AND -11
400
Write a rational function that has a hole at 4, VA at -2, and goes to zero for end behavior.
Answers will vary, but ex:
\frac{(x-4)}{(x-4)(x+2)}
400
Find the inverse and its domain for:
y=10^(2x-7)
Domain: (0,inf) (range of exponential functions with no vertical shifts)
f^-1(y)=\frac{log(y)+7}{2}
400
Given f(x) = log(3x-9) + 10
Find f-1(y) AND give domains for both f and f-1
f-1(y) = 1/3(10y-10+9)
D of f: (3, inf)
D of f-1 : (-inf, inf)
500
Sketch the function:
3(0.5x-1)2-2
500
Given: f(x)=log(x), g(x)=5x3+680, and h(x)=|6-5x|
Find: h(f(g(4))
9
500
In Burlington, WI - there used to be a place called the Sci-Fi Cafe. It was weird. Ms. Dexter went once with some high school friends and was told that you could summon fairies (well, only women could - sorry, guys) by putting out rings of M&Ms (this is not a joke - this really happened to her.) Ms. Dexter lays out a huge ring of M&Ms. Initially, she finds 10 fairies (this part did NOT actually happen). 4.5 weeks later, there are 83 fairies. Assuming exponential growth - what would be the r value in the model P=Poert model for this situation? Give 6 decimal places!
r = 0.470279
500
A population (in millions) is decreasing such that:
p(t) = 500 / (1 + e-0.065t) where t is measured in decades.
In how many years will the population reach 300 million? Round to the nearest hundredth.
62.38 years.
500
A population of introduced insects grows then declines based on the model below (x in years). When will there be 300 insects remaining in the reserve?
\frac{500(x+4)}{10x^2+6)
0.355 years
500
Find the inverse of:
y=ln(2x+1)
f^-1(y)=\frac{e^y-1}{2}
500
The Loggers stadium has 6000 seats and sells tickets for $13. At this price, they sell about 4,800 seats. Market research says that for each 50 cent decrease in price, they'll sell 50 more seats. Write an equation for the profit AND state the relevant domain.
Equation: (4800+50x)(13-0.5x)
D: (-96, 24) *Seat capacity