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MATH 115 EXAM 1 questions with correct answers
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MATH 115 EXAM 1 questions with correct answers
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MATH 115 EXAM 1Functions - 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)
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