What is a vertical asymptote?

A vertical asymptote is a vertical line x = a that the graph approaches as x approaches a

A vertical asymptote is a curve that intersects the function at multiple points.

A vertical asymptote is a horizontal line that the function approaches.

A vertical asymptote is a point where the function is defined.

What must be true for intermediate theorem to apply?

Must be continuous on the given interval

The function must take on every y-value between f(a) and f(b) somewhere between x=a and x=b

Must be continuous on f(a) and f(b)

Must be continuous on f(a)-f(b)/2 = f(c)

What do you do to a function to find a horizontal asymptote?

Take the limit as x approaches ∞ and as x approaches -∞

Highest exponent in the numerator over highest exponent in the denominator

Bottom heavy, top heavy, equivalent

Parentheses like this (a,b) mean...

Include everything in-between but the endpoints

Trick question, only [a,b] exists

If the limit of the denominator of a rational function approaches 0, then the function will have a vertical asymptote

True, it is always a Vertical Asymptote

As long as the denominator equals 1

$$\frac{d}{dx}$$ (f(x)=c) where c is a constant.

Trick question, this is a false statement

What must be true for the extreme value theorem to apply?

The function must be defined on a closed interval

The function must be continuous

The function must be defined on a open interval

The function must be differentiable

What is a critical point?

The x coordinate where the derivative does not exist

The x coordinate where the derivative is is 0

The y coordinate where the derivative is 0

The y coordinate where the derivative does not exist

an x-value where it is 0 or does not exis

a x-value where the slope is constant

a x-value where the second derivative is positive

a x-value where the function is increasing

If a function has one relative extrema

The function has one absolute extremum.

The function has no relative extrema.

The function has multiple relative extrema.

The function has two relative extrema.

The speed of a particle with position x(t) is increasing on (a, b) because:

x'(t) and x''(t) have the same sign on (a, b)

x'(t) and x''(t) have the different sign on (a, b)

x'(t) has the same time on x(t) same sign on (a, b)

x'(t) has the same time on x(t) different sign on (a, b)

The speed of a particle with position x(t) is decreasing on (a, b) because:

x'(t) and x''(t) have the different sign on (a, b)

x'(t) and x''(t) have the same sign on (a, b)

x'(t) has the same time on x(t) same sign on (a, b)

x'(t) has the same time on x(t) different sign on (a, b)

The function, f(x), is under approximated by a tangent line when:

f"(x) > 0 from the point of tangency to the point being approximated

f"(x) < 0 from the point of tangency to the point being approximated

The function, f(x), is over approximated by a tangent line when:

f"(x) < 0 from the point of tangency to the point being approximated

f"(x) > 0 from the point of tangency to the point being approximated

f(x) has a relative maximum at x = a because: (2nd derivative test)

f(x) has f''(a) = 0 and f''(a) = -

f(x) has f''(a) = 0 and f''(a) = +

f(x) has a relative minimum at x = a because: (2nd derivative test)

f(x) has f''(a) = 0 and f''(a) = +

f(x) has f''(a) = 0 and f''(a) = -

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Authored by Adam Pena

Mathematics

12th Grade

CCSS covered

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46 questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

True

False

Sometimes

Tags

CCSS.HSN.RN.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The graph of a function can never cross one of it's horizontal asymptotes

False

Sometimes

True

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

False

Sometimes

True

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The graph of any function can have two horizontal asymptotes

Sometimes

True

False

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Continuity

Discontinuity

Removable Discontinuity

Jump Discontinuity

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

∞

-∞

Tags

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.1

CCSS.HSG.C.B.5

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

∞

-∞

Tags

CCSS.HSF.TF.A.2

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