Precalc Exam 2 (2.1-3.6)

Function

a relation in which no two ordered pairs have the same domain and different ranges. Each x-value can only have one Y value.

Slope equation

m = (y2-y1) / (x2-x1)

Point-slope form

(y-y1) = m(x-x1)

slope intercept form

y = mx+b

general form

ax+by+c=0

midpoint formula

((x1+x2 / 2), (y1+y2 / 2))

distance formula

d = √((x2-x1)² + (y2-y1)²)

Is this a function: x² + y = 4

Yes!!

Is this a function: x² + y² = 4

No!!

Square root property

A² = b
A = ±√b

What is the proper notation of √-a?

(√a)i

Vertical Line Test

Graphs of functions must cross a vertical line only once, or not at all, at any given point.

Relative minima and maxima

Points at which a function changes direction- “turns around”.

Function where f(-x) = f(x)

Even function with y-axis symmetry

Function where f(-x) = -f(x)

Odd function with origin symmetry

Is this function even or odd? f(x) = x^5 + x³ + x - 5

Odd - it has all odd powers

Is this function even or odd? f(x) = x^6 - x^4 - x² + 7

Even - it has all even powers

Is this function even or odd? f(x) = x^7 + x^4 - x³ + 23

Neither - it has both even and odd powers

How to read this set notation? {x|x > y² + 6}

The set of all x-values where x is greater than the value of y²+6.

How to read this set notation? {y|y ≤ √27 - x}

The set of all y-values where y is less than or equal to the value of √27 - x.

Greatest integer function

Function where int(x) = the greatest integer that is less than or equal to x

Difference quotient equation

( f(x+h) - f(x) ) / h

Domain of a piecewise function(in interval notation)

(-3, inf) U {3}

(-inf, -5) U (-5, 11) U (11, inf)

The domain is a union of values from neg. infinity to -5; -5 to 11; 11 to infinity. Endpoints not included.

(-inf, -27] U [3, inf)

The domain is a union of values from neg. infinity to -27; 3 to infinity. -27 and 3 are included as values.

Conversion from point-slope to slope-intercept

Solve point-slope equation for Y

Slope of a constant function

0/y

Slope of an undefined function

Y/0

Equation of the line passing through (5,6) and parallel to the line y=4/5x + 2

(y - 6) = 4/5(x - 5)

Equation of the line passing through (8, 2) and perpendicular to the line y= 7x - ½

(y - 2) = -1/7(x - 8)

perpendicular slope

Negative reciprocal of given slope

The graph of f passes through (9,-7) and is perpendicular to the line with an x-intercept of 20 and a y-intercept of 45.

Traits of a constant function

F(x) = C

Domain: (-inf, inf)

Range: C

End behavior: constant approaching -inf and inf

Even

Traits of an identity function

F(x) = x

Domain: (-inf, inf)

Range: (-inf, inf)

End behavior: decreasing approaching -inf, increasing approaching inf

Odd