Intro to Functions and Function Behavior

Domain

How far left or right a graph goes

Range

How far up or down the graph goes

X-intercepts

Where the graph crosses the x-axis (#,0)

Y-intercepts

Where the graph crosses the y-axis (0,#)

Horizontal Asymptote

Where horizontal line graph approaches but does not touch

Vertical Asymptote

Vertical line graph that approaches but does not touch

Refelectional Symmetry

Object can reflect (flip) onto itself

Rotational Symmetry

Object can rotate onto itself

Linear Family** Parent Function**

y = x

Linear Family** General Form**

y = mx+b

Absolute Value Parent Function

y = |x|

Absolute Value General Form

y = a|x-h| + k

Quadratic Family Parent Function

y = x^2

Cubic Family** Parent Function**

y = x^3

Cubic Family** General Form**

y = a(x-h)^3 + k

Square Root Family** Parent Function**

y = \sqrt{x}

Square Root Family** General Form**

y = a\sqrt{x-h} + k

Cube Root Family** Parent Function**

y = \sqrt[3]{x}

Cube Root Family** General Form**

y = a\sqrt[3]{x-h} + k

Exponential Family** Parent Function**

y = b^x

Exponential Family** General Form**

y = ab^{x-h} + k

Logarithmic Family** Parent Function**

y = \log_b(x)

Logarithmic Family** General Form**

y = a\log_b(x-h) + k

Rational Family** Parent Function**

y = \frac{1}{x}

Rational Family** General Form**

y = \frac{a}{x-h} + k

Trigonometric Family (Sine)** Parent Function**

y = \sin(x)

Trigonometric Family (Sine)** General Form**

y = a\sin(b(x-h)) + k

Vertex

point where graph changes directions

Max/Min

Highest/lowest points of a graph

Axis of symmetry

Vertical line that splits parabola into two congruent halves

The axis of symmetry has the same value as

The x value for the vertex (h,k) (H)

Parabola

U Shape graph of a quadratic function

Zeroes of a function

X-ints of a function (roots or solutions)

Decreasing

Set of x values where the graph goes down left to right

Increasing

Set of x values where the graph goes up left to right

What situation best models a trigonometric function

When a value changes constantly (up and down and up and down in waves)

Quadratic Family General Form(s)

y = ax² + bx + c - Standard Form
y = a(x-h)² + k - Vertex Form
y = a (x-p)(x-q) - Intercept Form

Linear rate of change formula

y2 - y1/x2 - x1 OR rise/run

Nonlinear Rate of Change formula

Example of nonlinear rate of change formula

(100 × 0.97^60) - (100 × 0.97^30) /60-30 (x2 = 60, x1 = 30)

Exponential Decay vs Growth

When exponential function either goes up or down

Vertical translation

Represented by the k or b value for a function (mx + b, y = a(x-h)² + k)

Horizontal Translation

Represented by the h or m value for a function (mx + b, y = a(x-h)² + k)

Dilations

represented by the a value, there two types: strech and compression

Stretch Dilation

when a graph gets bigger (looks narrow) (a >1)

Compress Dilatation

when a graph gets smaller (looks compressed) (a<1)

Reflections

Transformation over the line of reflection

Represented by negative a value. ( a = -)