MATH 115 EXAM 1 questions with correct answers

MATH 115 EXAM 1

Functions - correct answer ✔✔One output for every input, must pass vertical line test,



Interval Notation - correct answer ✔✔( a , b ) = { x : a < x < b }

[a,b]={x:a≤x≤b}



Linear Functions - correct answer ✔✔f(x) = mx + b



Slope - correct answer ✔✔m = ∆y / ∆x

In words: For every additional unit of x, y increases/decreases by m units



Monotonicity - correct answer ✔✔Function either entirely increases or decreases; parabolas don't have



Proportionality - correct answer ✔✔y = kx where k ≠ 0



Concave Up - correct answer ✔✔U shape ; graph bends upwards moving left to right



Concave Down - correct answer ✔✔n shape ; graph bends downwards moving left to right



Exponential Functions - correct answer ✔✔P = P₀a^t

When a > 0, exponential growth

When a < 0, exponential decay

P₀ = initial value

a = growth/decay factor

t = time

, Half Life Formula - correct answer ✔✔N = N₀(1/2)^(t/hl)

hl = half life



Exponential Functions with Base e - correct answer ✔✔P = P₀e^kt

When k > 1, exponential growth

When k < 1, exponential decay

e^k = a

Continuous



Horizontal Shift - correct answer ✔✔y = f(x ± k)



Vertical Shift - correct answer ✔✔y = f(x) ± k



Reflection Over x-axis - correct answer ✔✔y = -f(x)



Reflection Over y-axis - correct answer ✔✔y = f(-x)



Vertical Stretch - correct answer ✔✔y = kf(x) where k > 1



Vertical Shrink - correct answer ✔✔y = kf(x) where k < 1



Horizontal Stretch - correct answer ✔✔y = f(kx) where 0 < k < 1



Horizontal Shrink - correct answer ✔✔y = f(kx) where k > 1



Even Functions - correct answer ✔✔f(-x) = f(x)

Symmetric about y axis



Odd Functions - correct answer ✔✔f(-x) = -f(x)