AP Calc AB - Pretest

What is necessary after square rooting a value?

±

if something is raised to ¾ how do you undo it?

raise it to ^4/3

How to determine VA?

factor the numerator and denominator, cancel common factors, and set the remaining denominator equal to zero

How to determine HA?

numerator degree = denominator degree: The horizontal asymptote is y = a/b where a and b are the leading coefficients of the numerator

Numerator degree (m) < Denominator degree (n): The horizontal asymptote is y = 0

Numerator degree (m) > Denominator degree (n): There is no horizontal asymptote

Remainder Theorm

when a polynomial f(x) is divided by a linear factor (x - a), the remainder of that division is equal to the value of the function evaluated at a, written as f(a)

What does a rational look like

What does a exponential look like

What does a logarithmic look like

What does a square root look like

difference of two cubes

a³ - b³ = (a - b)(a² + ab + b²)

sum of two cubes

a³ + b³ = (a + b)(a² - ab + b²)

(x-y)²

x²-2xy+y²

(x+y)²

x²+2xy+y²

Even Functions

a function where substituting a negative input gives the exact same output as the positive input, satisfying the rule f(-x) = f(x)

Symmetric across the y-axis

Odd Functions

a mathematical function that yields a negative output when you input a negative value, satisfying the rule f(-x) = -f(x)

Symmetry about the origin

Change of Base Formula

Standard Form

Ax+By+C=0

multiplying powers of the same base

(x^a)(x^b) = x^(a+b)

Trig identities

sin²x + cos²x = 1

tan²x + 1 = sec²x

1 + cot²x = csc²x

how to find x-int of logarithms

• Set \(y = 0\): Replace \(f(x)\) or \(y\) with \(0\) in the function equation.

• Isolate the logarithm: Move any outside constants or coefficients to the other side so that the log expression stands alone.

• Convert to exponential form: Rewrite \(\log_b(A) = c\) as \(b^c = A\) using the definition of a logarithm.

• Solve for \(x\): Use basic algebra to find the final value of \(x\).

• Check the domain: Ensure your answer makes the inside of the logarithm (the argument) greater than zero

when do you limit the domain for inverses?

you limit the domain when you make a inverse from a square root

You restrict the domain to x>=0 or x<=0 so the parabola's inverse becomes a single-valued square root function instead of plus-or-minus

Which trig functions are even?

cos

sec

Which trig functions are odd?

tan

cot

sin

csc

what does in terms of x mean

that they only variable used is x

what does the argument of a logarithm need to be?

greater than 0

parts of a logarithm

sin function

cos function

y = Acos(Bx+C) + D