Unit 1.1 change in tandem

Unit 1.1:

A. Function Basics

Function = one input → one output

Vertical line test:

more than 1 hit → NOT a function

B. Intercepts

x-intercept → y=0y = 0y=0

y-intercept → x=0x = 0x=0

C. Increasing / Decreasing (DIRECTION)

Increasing → graph goes UP

Decreasing → graph goes DOWN

D. Positive / Negative (POSITION)

Positive → above x-axis

Negative → below x-axis

E. Rate of Change (Slope)

f(b)−f(a)b−a\frac{f(b) - f(a)}{b - a}b−af(b)−f(a)​

Positive slope → increasing

Negative slope → decreasing

F. Concavity (SHAPE — MOST IMPORTANT)

Concave UP → slope increasing → ∪

Concave DOWN → slope decreasing → ∩

G. KEY CONNECTION (THIS IS EVERYTHING)

Given

Meaning

Positive rate

increasing

Negative rate

decreasing

Increasing rate

concave up

Decreasing rate

concave down

H. Real-World Translation

Narrow → rises faster

Wide → rises slower

Constant width → straight line

Memorize THIS:

Up/down = direction

Above/below = sign

Steeper/flatter = concavity