MATH 101i Final Review

GeneralFunction

100

The minimum and maximum of the graphically defined function f

min: (-1,-3)

max: (2,5)

200

What are the domain and range of the graphically defined function f?

Domain:[-2,4]

Range: [-3,0)U[1,5]

300

Using transformations, plot g(x)=2|x-1|+1

vertex at (1,1)

slope 2

400

f(x)=x²+2

g(x)=2x+1

Simplify the function composition f(g(x))

f(g(x))=4x²+4x+3

Linear Functions

100

Graph the following linear function

y=-3x+1

slope: -3

y intercept: 1

200

If the population of a town is approximated by the linear function

P(t)=4500+250t in years since 2000, when will there be about 5000 people?

t=2

Year: 2002

300

Find the equation of the line through the points (1,2) and (9,3)

y=1/8(x-1)+2

y=1/8x+15/8

400

Use the table to find the average rate of change of ladybug births between 1995 and 2025?

AROC: 62.6 Ladybug Births / Year

Quadratic Functions

100

Write the quadratic in vertex form

2x²+8x+1

2(x²+4x+4)-8+1

2(x+2)²-7

200

Solve the quadratic

x²+x=3x-1

x²-2x+1=0

(x-1)²=0

x=1

300

Solve the quadratic

2x²-3x-2=0

(2x+1)(x-2)=0

x=-1/2 or x=2

400

The trajectory of dropped object is given by

h(t)=-16t²+h₀ where h is in feet where t is in seconds

If the object hits the floor at t=3 s, what was the initial height h₀?

h(3)=0

144 ft

Exponents and Logs

100

Use the compound interest formula P(t)=P₀(1+r/n)^nt to find how much is in an account with an Initial amount = $400 and Yearly Interest rate = 3% after 1 year of monthly compounding.

400(1+.03/12)^12*1 = $412.17

200

Use the simple interest formula P(t)=P₀(1+rt) to find how much is in an account after two years with an initial amount = $400 and a yearly interest rate = 3%

400(1+.03*2)= $424

300

A continuously compounded bank account starts with $100. With a yearly interest rate of r=5%, how long will it take for the initial amount to triple?

Almost 22 years

400

Solve the logarithmic equation

ln(x+1)+ln(x-1)=2ln(1)

No Solutions