Week 1 MA-121

Question 1

Quadratic Functions General Form

Accepted Answer

f(x) = ax^2 + bx + c, where a ≠ 0

Question 2

Quadratic Functions Axis of Symmetry

Accepted Answer

x = -b/2a

Question 3

Quadratic Functions General Form Vertex

Accepted Answer

(-b/2a, f(-b/2a))

Question 4

Quadratic Functions: Parabola opens upward if...

Accepted Answer

a > 0 (vertex is global minimum)

Question 5

Quadratic Functions: Parabola opens downward if...

Accepted Answer

a < 0 (vertex is global maximum)

Question 6

Quadratic Functions Range: If a > 0

Accepted Answer

[f(-b/2a), ∞]

Question 7

Quadratic Functions Range: If a < 0

Accepted Answer

[-∞, f(-b/2a)]

Question 8

Quadratic Functions Domain

Accepted Answer

(-∞, ∞)

Question 9

Quadratic Functions Standard Form

Accepted Answer

f(x) = a(x-h)^2 + K

Question 10

Quadratic Functions Standard Form Vertex

Accepted Answer

(h,k) where h = -b/2a and k = f(-b/2a)

Question 11

Quadratic Functions: Quadratic Equations

Accepted Answer

x = quadratic formula

Question 12

Quadratic Functions (Quadratic Equations): b^2 - 4ac = 0

Accepted Answer

One zero (multiplicity 2)

Question 13

Quadratic Functions (Quadratic Equations): b^2 - 4ac > 0

Accepted Answer

Two distinct real zeros

Question 14

Quadratic Functions (Quadratic Equations): b^2 - 4ac < 0

Accepted Answer

No real zeros

Question 15

Polynomial Functions Graphical Behavior

Accepted Answer

End behavior depends on leading term Zeros (x-intercepts) and multiplicities affect shape

Question 16

Rational Functions General Form

Accepted Answer

f(x) = p(x)/q(x) where Q(x) ≠ 0

Question 17

Rational Functions Domain

Accepted Answer

All Real Numbers except when denominator = 0

Question 18

Rational Functions: Vertical Asymptotes

Accepted Answer

Found at 0's of Q(x) after simplifying p(x)/q(x)

Question 19

Rational Functions: Removeable Discontinuities

Accepted Answer

Occur at canceled factors in denominator

Question 20

Rational Functions (Horizontal asymptotes): Degree of num < denom

Accepted Answer

y = 0

Question 21

Rational Functions (Horizontal asymptotes): Degrees equal

Accepted Answer

y = lead coefficient of P / lead coefficient of Q

Question 22

Rational Functions (Horizontal asymptotes): Degree of num > denom by 1

Accepted Answer

Slant asymptote

Question 23

One-Sided Limits from the Left

Accepted Answer

lim x->a- f(x)=L

Question 24

One-Sided Limits from the Right

Accepted Answer

lim x->a+ f(x) = L

Question 25

Two-Sided Limits

Accepted Answer

lim x->a f(x) = L if x->a- f(x) = L and x->a+ f(x) = L

Question 26

Infinite Limits (lim x->a f(x) = +- ∞)

Accepted Answer

Vertical asymptote at x = a

Question 27

Limit Laws Sum

Accepted Answer

lim x->a (f(x)+g(x)) = lim x->a f(x) + limx->a g(x)

Question 28

Limit Laws Difference

Accepted Answer

lim x->a (f(x) - g(x)) = limx->a f(x) - limx->a g(x)

Question 29

Limit Laws Product

Accepted Answer

lim x->a (f(x) * g(x)) = lim x->a f(x) * lim x->a g(x)

Question 30

Limit Laws Quotient

Accepted Answer

lim x->a (f(x) / g(x)) = lim x->a f(x) / lim x->a g(x), g(x) ≠ 0

Week 1 MA-121

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