AP Pre-Calc Memorization Test

Vertical Asymptotes of Sec(x)

Vertical Asymptotes of Sec(x)

Vertical Asymptotes of Csc(x)

Functions change at an increasing rate whenever they are _______

Concave Up

Functions change at a decreasing rate whenever they are_______

Concave Down

Write the limit in proper notation for a function whose y-values increase towards ∞ as its x-values decrease toward -∞:

Lim (x→-∞), F(x)=∞

Average rate of change formula is?

f(b)-f(a)

---

b-a

Lim (x→∞), f(x)=3 OR Lim (x→-∞), f(x)=3

Write a limit that proves a function f has a horizontal asymptote at y = 3

Write a limit that proves a function f has a vertical asymptote at x = 3

Lim (x→3⁺), f(x)=∞ OR Lim (x→3^-), f(x)=∞

Vertical asymptotes are found where the _____________ __ ________________.

denominator is zero

Holes are found where the ________________ _ _________________ are _______________.

denominator & numerator are zero

If numerator degree > denominator degree, the horizontal asymptote is

NON-EXSITING ( no horizontal asymptote)

If numerator degree < denominator degree, the horizontal asymptote is

y=0

If numerator degree = denominator degree, the horizontal asymptote is

y=ratio of leading coefficients

Slant asymptotes are found using

long division

What does the negative in front of a represent in the following: y = −a • f (−b ( x + c ) ) + d

Reflect over the x-axis

What does the a represent in the following: y = −a • f (−b ( x + c ) ) + d

the Vertical Dilation

What does the negative in front of b represent in the following: y = −a • f (−b ( x + c ) ) + d

reflect over the y-axis

What does the b represent in the following: y = −a • f (−b ( x + c ) ) + d

The Horizontal Dilation

What does the c represent in the following: y = −a • f (−b ( x + c ) ) + d

the Horizontal translation

What does the d represent in the following: y = −a • f (−b ( x + c ) ) + d

the Vertical translation

What is the definition of an even function f:

F(-x)= F(x)

What is the definition of an odd function f:

F(-x)= -F(x)

An arithmetic sequence grows ______________.

linearly

General form of an arithmetic sequence:

a_n=a₁ + (n-1)d

Definition of common deference:

difference between consecutive terms

A geometric sequence grows

exponentially

General form of a geometric sequence:

a_n = a₁ ( r ) ^n-1

Definition of common ratio:

Constant proportional change between terms

General equation of a linear function in point-slope form:

y - y₁ = m( x-x₁ )

General equation of an exponential function:

y= a • b^x

Exponential growth functions have a common ratio that is

greater than 1

Exponential decay functions have a common ratio that is

between 0 and 1

Finish the exponent rule: a^xa^y =

a^x+y

Finish the exponent rule: a^x/a^y =

a^x-y

Finish the exponent rule: (a^x)^y =

a^xy

Finish the exponent rule: a^xb^x =

(ab)^x

Finish the exponent rule: (a/b)^x =

(a^x) / (b^x)

Finish the exponent rule: a^-x =

1 / a^x

f(g(x)) means to substitute __________ into ____________.

g(x) into f(x)

Composing a function with its inverse results in _________.

x

Algebraically find the inverse of a function by _________________.

swapping x & y, then solving for y

The inverse of a function is a reflection over _________

y=x

The domains and ranges of inverse functions are ________

swapped

a^c = b can be rewritten as a logarithm in the following way:

log_ab = c

Finish the logarithm property: log_a(xy) =

log_ax + log_ay

Finish the logarithm property: log_a(x/y) =

log_ax - log_ay

Finish the logarithm property: b • log_ax =

log_ax^b

Finish the logarithm property: log_bx =

log_ax/log_ab (change of base formula)

Formula for a coordinate point on a circle with radius r:

(rcosθ, rsinθ)

State the value of the trigonometric function in terms of x and y on the unit circle:

sin(θ) =

y

State the value of the trigonometric function in terms of x and y on the unit circle:

cos(θ) =

x

State the value of the trigonometric function in terms of x and y on the unit circle:

tan(θ) =

y/x

State the value of the trigonometric function in terms of x and y on the unit circle:

sec(θ) =

1/x

State the value of the trigonometric function in terms of x and y on the unit circle:

csc(θ) =

1/y

State the value of the trigonometric function in terms of x and y on the unit circle:

cot(θ) =

x/y

State the formula for finding the period of the trigonometric function in terms of b: period of sin(θ) =

2π/b

State the formula for finding the period of the trigonometric function in terms of b: period of cos(θ) =

2π/b

State the formula for finding the period of the trigonometric function in terms of b: period of tan(θ) =

π/b

State the formula for finding the period of the trigonometric function in terms of b: period of sec(θ) =

2π/b

State the formula for finding the period of the trigonometric function in terms of b: period of csc(θ) =

2π/b

State the formula for finding the period of the trigonometric function in terms of b: period of cot(θ) =

π/b

State the reciprocal of the trigonometric function: sin(θ)

cscθ

State the reciprocal of the trigonometric function: cos(θ)

secθ

State the reciprocal of the trigonometric function: tan(θ)

cotθ

State the reciprocal of the trigonometric function: sec(θ)

cosθ

State the reciprocal of the trigonometric function: csc(θ)

sinθ

State the reciprocal of the trigonometric function: cot(θ)

tanθ

State the three Pythagorean identities:

1) sin²θ+ cos²θ = 1

2) 1+ tan²θ = sec²θ

3) 1 + cot²θ = csc²θ

State the four double angle identities:

1) sin(2θ)= 2sinθ cosθ

2) cos(2θ)= cos²θ - sin²θ

3) cos(2θ)= 2cos²θ -1

4) cos(2θ)= 1-2sin²θ

State the two sum and deference identities:

1) sin(A±B)=sinAcosB±cosAsinB

2) cos(A±B)= cosAcosB±sinAsinB

Write the polar equations for r and 1 in terms of x and y:

r= square root of (x² + y²)

θ= tan^-1(y/x)

Write the two general forms of rose curves, as well as the rules for n:

r= a sin(nθ)

r= a cos(nθ)

If n is odd: _________________________

n= number of petals

If n is even: _________________________

2n= number of petals

Write the two limacon equations r, in terms of sine and cosine:

r= a ± b cosθ

r= a ± b sinθ

For r= a ± b cosθ & r= a ± b sinθ , state the relationship between a and b that determines Inner loop present:

|a| < |b|

For the r= a ± b cosθ & r= a ± b sinθ , state the relationship between a and b that determines Heart shape (cardioid):

|a| = |b|

For the r= a ± b cosθ & r= a ± b sinθ , state the relationship between a and b that determines dented:

|a| > |b|

For the r= a ± b cosθ & r= a ± b sinθ , state the relationship between a and b that determines Max Radius:

|a| + |b|

For the r= a ± b cosθ & r= a ± b sinθ , state the relationship between a and b that determines Min Radius:

|a| - |b|

Sketch f(x) = sin x

Sketch f(x) = cos x

Sketch f(x) = tan x

Sketch f(x) = e^x

Sketch f(x) = lnx

Sketch f(x) = arcsinx

Sketch f(x) = arccos x

Sketch f(x) = arctan x

What are the trig functions that are positive in quadrant II of the unit circle:

sine & cosecant

What are the trig functions that are positive in quadrant III of the unit circle:

tangent & cotangent

What are the trig functions that are positive in quadrant IV of the unit circle:

cosine & secant

What are the coordinate points for quadrant I of the unit circle

What are the coordinate points for quadrant II of the unit circle

What are the coordinate points for quadrant III of the unit circle

What are the coordinate points for quadrant IV of the unit circle