MATH 115 EXAM 1 QUESTIONS ANSWERED CORRECTLY LATEST
UPDATE 2026
Functions - Answers One output for every input, must pass vertical line test,
Interval Notation - Answers ( a , b ) = { x : a < x < b }
[a,b]={x:a≤x≤b}
Linear Functions - Answers f(x) = mx + b
Slope - Answers m = ∆y / ∆x
In words: For every additional unit of x, y increases/decreases by m units
Monotonicity - Answers Function either entirely increases or decreases; parabolas
don't have
Proportionality - Answers y = kx where k ≠ 0
Concave Up - Answers U shape ; graph bends upwards moving left to right
Concave Down - Answers n shape ; graph bends downwards moving left to right
Exponential Functions - Answers 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 - Answers N = N₀(1/2)^(t/hl)
hl = half life
Exponential Functions with Base e - Answers P = P₀e^kt
When k > 1, exponential growth
When k < 1, exponential decay
e^k = a
Continuous
Horizontal Shift - Answers y = f(x ± k)
Vertical Shift - Answers y = f(x) ± k
Reflection Over x-axis - Answers y = -f(x)
Reflection Over y-axis - Answers y = f(-x)
Vertical Stretch - Answers y = kf(x) where k > 1
Vertical Shrink - Answers y = kf(x) where k < 1
Horizontal Stretch - Answers y = f(kx) where 0 < k < 1
Horizontal Shrink - Answers y = f(kx) where k > 1
Even Functions - Answers f(-x) = f(x)
Symmetric about y axis
Odd Functions - Answers f(-x) = -f(x)
Symmetric about the origin
Inverse Functions - Answers Invertible iff each input has only one output both ways;
must pass horizontal line test; y = f(x) ↔ y = f⁻¹(x)
Logarithm Functions - Answers Increase more slowly than exponential functions; y =
a^x ↔ x = log(base a)y
Properties of Logarithmic Functions - Answers log(base a)(x/y) = log(base a)(x) -
log(base a)(y)
log(base a)(xy) = log(base a)(x) + log(base a)(y)
log(base a)(x)ⁿ = nlog(base a)(x)
log(base a)(1) = 0
log(base a)a = 1
UPDATE 2026
Functions - Answers One output for every input, must pass vertical line test,
Interval Notation - Answers ( a , b ) = { x : a < x < b }
[a,b]={x:a≤x≤b}
Linear Functions - Answers f(x) = mx + b
Slope - Answers m = ∆y / ∆x
In words: For every additional unit of x, y increases/decreases by m units
Monotonicity - Answers Function either entirely increases or decreases; parabolas
don't have
Proportionality - Answers y = kx where k ≠ 0
Concave Up - Answers U shape ; graph bends upwards moving left to right
Concave Down - Answers n shape ; graph bends downwards moving left to right
Exponential Functions - Answers 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 - Answers N = N₀(1/2)^(t/hl)
hl = half life
Exponential Functions with Base e - Answers P = P₀e^kt
When k > 1, exponential growth
When k < 1, exponential decay
e^k = a
Continuous
Horizontal Shift - Answers y = f(x ± k)
Vertical Shift - Answers y = f(x) ± k
Reflection Over x-axis - Answers y = -f(x)
Reflection Over y-axis - Answers y = f(-x)
Vertical Stretch - Answers y = kf(x) where k > 1
Vertical Shrink - Answers y = kf(x) where k < 1
Horizontal Stretch - Answers y = f(kx) where 0 < k < 1
Horizontal Shrink - Answers y = f(kx) where k > 1
Even Functions - Answers f(-x) = f(x)
Symmetric about y axis
Odd Functions - Answers f(-x) = -f(x)
Symmetric about the origin
Inverse Functions - Answers Invertible iff each input has only one output both ways;
must pass horizontal line test; y = f(x) ↔ y = f⁻¹(x)
Logarithm Functions - Answers Increase more slowly than exponential functions; y =
a^x ↔ x = log(base a)y
Properties of Logarithmic Functions - Answers log(base a)(x/y) = log(base a)(x) -
log(base a)(y)
log(base a)(xy) = log(base a)(x) + log(base a)(y)
log(base a)(x)ⁿ = nlog(base a)(x)
log(base a)(1) = 0
log(base a)a = 1
