Math 141 Exam 3 Review - Spring

Exponential Function Facts

100

What are the:

Domain of exponential functions

Range of exponential functions

Domain: (-∞,∞), All reals, ℝ

Range: (0,∞) {y|0<y}

200

Name two points on an exponential function graph

(0,1) and (1, b)

300

What does y=0 represent?

Horizontal Asymptote

400

What determines exponential growth or decay in terms of the base?

Growth: 1 < b

Decay: 0 < b < 1

500

What term describes exponential functions? or What is the relationship of the inputs and outputs of an exponential function?

1:1, 1-1, one-to-one

Formulas and Definitions

100

Write the definition of Exponential functions

f(x)=a^x 

200

Write the compound interest formula

A=P(1+r)^t

300

Write the continuous interest formula

A=Pe^rt

400

Write the definitions of even and odd functions;

Bonus (100 (50 each)): include graphical symmetry for each

Even: f(-x)=f(x) symmetric with respect to the y-axis

Odd: -f(x)=f(-x) symmetric with respect to the origin; point (0,0)

500

Write the three definitions of logs

log v = u exactly when v=10^u

log_b v = u exactly when v=b^u

ln v = u exactly v=e^u

Log Laws

100

What are the standard bases of the log and ln functions?

log = base 10 and ln = base e

200

What is the product rule of logarithms?

Log_b(MN)=Log_b(M)+Log_b(N)

300

What is the quotient rule of logarithms?

Log_b(M/N)=Log_b(M)-Log_b(N)

400

What is the power rule of logarithms?

Log_b(M^k)=kLog_b(M)

500

What is the change of base formula?

Logb(M)=	Loga(M)
	Loga(b)

Solve: Roots and Radicals

100

Simplify √243 + √48

9√3 + 4√3

200

Solve √1-2x -7=x

x=-4

300

Solve: ∛7-6x=3

x=-10/3

400

Factor: x^(2/3)-2x^(1/3)-15

(x^(1/3)-5)(x^(1/3)+3)

500

Rationalize the denominator:

f(x)=	2
	3+√6

f(x)=	6-2√6
	3

Solve: Logs and Exponentials

100

x⁴+2=94

∜92

200

log₇(∛7)

1/3

300

Write as a single logarithm:

3log₃(3) + log₃(7)

log₃(189)

400

Find the domain of:

f(x)=6xlog(7x-2)

Answer in interval notation

D_f = (2/7, ∞)

500

e^5-2√x = 48

x=	(-	ln(48)-5	)2
		2