Precalculus Review: Part 1 & 2 (Video Notes)

Fill-in-the-blank flashcards covering linear equations, inequalities, absolute value, functions, domain, transformations, and trigonometry concepts from the lecture notes.

A linear equation in x has the form __, where a, b, and c are constants.

ax + b = c

An inequality compares two values. a ≥ b means that a is __.

greater than or equal to b

For the equation x^3 − x^2 = 0, the solutions are x = __.

0 or 1

If a < 0, |a| equals __.

-a

Compute |−4| = __.

4

A function describes a relationship where every input has exactly one __.

output

The domain of f(x) = (x − 2)/(x − 1) is all real numbers except __.

1

The domain of g(x) = √(x^2 − 5x) is __.

(-∞, 0] ∪ [5, ∞)

If f(x) = x^2 − 2 and g(x) = 2x, then (fg)(x) = __.

2x^3 − 4x

A function is increasing on an interval I if when x1 < x2, f(x1) < f(x2); a function is __ on I if when x1 < x2, f(x1) > f(x2).

decreasing

f(x) = 1 + e^{x} is an example of an __ function.

exponential

When graphing y = 2 − √x − 1, perform a horizontal shift first, then reflect, and last do a __.

vertical shift

Let P(x, y) be a point on the terminal side of θ and r = √(x^2 + y^2). Then sin θ = y/r and cos θ = __.

x/r

On the unit circle, for θ = π/6, sin θ = __.

1/2

On the unit circle, for θ = π/6, cos θ = __.

√3/2

At θ = 0, sin θ = __.

0

At θ = 0, cos θ = __.

1

The graph y = sec x is the reciprocal of y = __.

cos x

The Pythagorean identity sin^2 x + cos^2 x = __.

1

csc x = __.

1/sin x

The solutions to 2 cos^2 x − √3 cos x = 0 on 0 < x < 2π are x = __.

π/2, 3π/2, π/6, 11π/6