Queenie’s Precalculus Final Review

Transformations of Functions

100

what is an equation for a quadratic function shifted down by 2?

f(x)=x²-2

200

what is an function for a quadratic equation with a vertical stretch of 2 and a horizontal shift right 3?

f(x)=2(x-3)²

300

what is an equation for the absolute value function shifted to the left by 20?

f(x)=|x+20|

400

what is an equation for the quadratic function shifted up by 5, to the right by 4, and reflected across the x-axis?

f(x)= - (x-4)^2-5

500

A function, f(x)= -4(x+3)²-5, is shifted up by 3 and translated left 2 units. what is the equation of the new function?

f(x)= - 4(x+5)²-2

Exponentials and Logarithms

100

which of the following functions will increase faster?

f(x)=4*5^x

h(x)=4*6^x

h(x)

200

log₁₀(10)+log₂(32)=

6

300

log₄(8)+log₄(32)=

4

400

The function f is given by f(x)=9*25^x.  Which of the following is an equivalent form for f(x)?

A. f(x)=3*5^(x/2)

B. f(x)=3*5^(2x)

C. f(x)=9*5^(x/2)

D. f(x)=9*5^(2x)

D. f(x)=9*5^(2x)

500

Which of the following is equivalent to 2(lnx) - 3ln(y) ?

A. ln(x²/y³)

B. ln(x²y³⁾

C. ln(2x-3y)

D. ln(2x/3y)

A. ln(x²/y³)

Formulas

100

What is the formula for the Pythagorean Theorem?

a²+b²=c²

200

What is the formula for Law of Sine?

sin(A)/a = sin(B)/b = sin(C)/c

300

What is the formula for Law of Cosine?

c²=a²+b²-2ab Cos(C)

400

What is the standard form for a linear equation?

ax+by=c

500

What is the inverse function property?

f(f^-1(x))=x

f^-1(f(x))=x

Calculate Trig Functions

100

cos(120)=

-1/2

200

tan(135)=

-1

300

arccos(-1)

pie

400

arctan(1)=

pie/4

500

arcsin(1)+arccos(0)

pie

Solve for the inverse

100

How do we call the inverse of cosine?

arccosine

200

What is the inverse function of ln(x)?

f(x)=e^x

300

Find the inverse of f(x)=3x-4

f^-1(x)=x/3+4/3

400

what is the axis of symmetry between a function and its inverse function?

y=x

500

Describe how to find the inverse function of f(x) in words.

(1) set function f(x) = y

(2) write x in terms of y (solve for x)

(3) switch x and y (interchange the variables)