Exam 2 Review

Transformations

100

For the function f(x), t(x)+c represents this transformation.

Vertical Shift by c units

200

For the function f(x), t(x+c) represents this transformation.

Horizontal Shift by -c

300

For the function f(x), c*t(x) represents this transformation.

Vertical Strech by a factor of c units.

400

For the function f(x), t(cx) represents this transformation.

Horizontal Stretch by a factor of 1/c

500

Name all transformations in the function f(x)=a*t(b(x+c/b))+d

• Horizontal Shift by -c/b
• Horizontal Stretch by 1/b
• Vertical Shift by d
• Vertical Stretch by a

Inverse Functions

100

A function is invertible if:

Each output has exactly one input; the function has the property that is 1-1

200

The point (-1,2) is on f(x). Where is the equivalent point on f^-1(x)?

(2,-1)

300

The function f(x) has a Domain of [-3,9) and a Range of [-4,5). What are the Doman and Range of ^f-1(x)

Domain f^-1(x): [-4,5)

Range f^-1(x): [-3,9)

400

What is the inverse of f(x)=2x+3

f^-1(x)=(x-3)/2

500

What is the inverse of f(x)=4+sqrt(2x-9)

f-1(x)=((x-4)²+9)/2

Exponential Function Facts

100

Domain of exponential functions:

(-∞,∞), All reals, ℝ

200

Range of exponential functions

(0,∞) {y|0<y}

300

Name two points on a graph of exponential functions (form: f(x)=a^x) used to find the model.

(0,1) and (1, a)

400

What does y=0 represent?

Horizontal Asymptote

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 Functions

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

Bob Loglaw's Log Blog

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(Mk)=kLog_b(M)

500

What is the change of base formula?

Log_b(M)=Log_a(M)/Log_a(b)