Free Printable On Ramps Unit 5 Precalc Review

1.

Simplify the rational function

a)

1/(x + 5)

b)

1/(x - 5)

c)

(x - 5)(x + 5)

d)

(x - 5)/[(x - 5)(x + 5)]

2.

(x²+11x+24)/(x²+4x-32)

a)

A.(x+7)/(x+4)

b)

B.3/4

c)

C.(x+3)/(x+4)

d)

D.(x+3)/(x-4)

3.

What is the X-Intercept?

a)

x= 0

b)

x= 4

c)

x= 5

d)

x= -5

4.

What are the x-intercepts?

a)

x= 2/3

b)

x= 4, x = -2

c)

x= -8, x = 1

d)

x= -4, x = 2

5.

What is the horizontal asymptote to this function?

a)

y=4

b)

y=0

c)

y=-2

d)

y=1

6.

Find the horizontal asymptote:

a)

y = 0

b)

y = 1

c)

None

d)

y = 3/2

7.

What is the Vertical Asymptotes?

a)

x= -4

b)

x= -4,5

c)

x= -5,5

d)

x= 4

8.

A vertical asymptote is found by setting the _________= to zero and solving for x

a)

Numerator

b)

Denominator

c)

Right side

d)

Left side

9.

How do you find the y-intercept?

a)

replace all x-values with 0

b)

replace all y-values with 0

c)

set denominator equal to 0

d)

compare the degrees of the numerator and denominator

10.

How do you find the x-intercept?

a)

replace all x-values with 0

b)

replace the y-value with 0 or make the numerator equal 0

c)

set denominator equal to 0

d)

compare the degrees of the numerator and denominator

11.

How do you determine the Horizontal Asymptote?

a)

replace all x-values with 0

b)

replace the y-value with 0 or make the numerator equal 0

c)

set denominator equal to 0

d)

compare the degrees of the numerator and denominator

12.

How do you know if a factor in the denominator is a hole instead of a V.A. ?

a)

It cancels out

b)

it equals 0

c)

you set the numerator equal to 0

d)

you compare the degrees

13.

When finding the H.A., if the numerator degree is greater than the denominator degree, the answer is...

a)

y = 0

b)

none

c)

y =a / b

d)

What's an H.A.?

14.

When finding the H.A., if the numerator degree is equal to the denominator degree, the answer is...

a)

y = 0

b)

none

c)

y =a / b

d)

What's an H.A.?

15.

The first thing you should do to find all the attributes for a rational function is...

a)

Factor it all out

b)

Find the V.A.

c)

Find the H.A.

d)

Find the x / y intercepts

16.

The horizontal asymptote equals zero when:

a)

the degree of the numerator and denominator are equal

b)

the degree of the numerator is less than the degree of the denominator

c)

the degree of the numerator is greater than the degree of the denominator

d)

the numerator equals zero

17.

What is the vertical asymptote?

a)

x = 2

b)

y = 2

c)

x = 1

d)

y = 1

18.

What are the excluded vales of this function?

a)

$-3$ only

b)

$1$ only

c)

$-3\ and\ 2$

d)

$-3\ and\ 1$

e)

$1\ and\ 2$

19.

What are the Vertical Asymptotes of...

a)

x = 0, -5

b)

x=0, 5

c)

x = 2, -7

d)

x = -2, 7

20.

Find the coordinates of the hole.

a)

(-3, -3)

b)

(-3, 3)

c)

(3, -3)

d)

(3, 3)

21.

Which graph is the function:

$f\left(x\right)=\frac{2x^2+14x}{x^2-4x}$

a)

b)

c)

d)

22.

What is the equation of the graph?

a)

b)

c)

d)

23.

What is the equation of the graph?

a)

b)

c)

d)

24.

$f\left(x\right)=\frac{2x-8}{x^2-16}$

What is the reason that this function does not have any x-intercepts?

a)

The function is not factorable.

b)

There is a hole on the x-axis where the x-intercept would go.

c)

Once simplified, there is no variable in the numerator

d)

There is a vertical asymptote at y=0.

e)

The degree of the numerator is less than the denominator.

25.

Choose all of the functions that have a horizontal asymptote at y=1

a)

$f\left(x\right)=\frac{x^2}{x^2-1}$

b)

$f\left(x\right)=\frac{x^2+5}{x+5}$

c)

$f\left(x\right)=\frac{2x\left(x-4\right)}{\left(x+1\right)\left(2x-3\right)}$

d)

$f\left(x\right)=\frac{3x}{3x^2-3}$

26.

What is the y-intercept for $f\left(x\right)=\frac{\left(x-3\right)\left(x-4\right)}{\left(x+1\right)\left(x-2\right)}$ ?

a)

(0,3) and (4,0)

b)

(0,-6)

c)

(0,6)

d)

(0,7)

e)

no y-intercept

27.

Select all the functions that have a slanted asymptote?

a)

b)

c)

d)

28.

Find the oblique asymptote.
(x²- 2x - 8) / (x - 2)

a)

y = x

b)

y = x - 8

c)

y = x - 4

d)

y = x + 4

29.

Identify the Oblique Asymptote for this function.

a)

y = 5x - 7

b)

y = 5x + 13

c)

y = 5x + 3

d)

y = 5x + 7

30.

What is the limit of the function as x approaches -4 from the left?

a)

2

b)

-4

c)

DNE

d)

-2

31.

Find $\lim_{x\rightarrow2^-\ }f\left(x\right)$

a)

-1

b)

5

c)

0

d)

DNE

32.

Find $\lim_{x\rightarrow2^+\ }f\left(x\right)$

a)

-1

b)

5

c)

0

d)

DNE

33.

Find $\lim_{x\rightarrow2\ }f\left(x\right)$

a)

-1

b)

5

c)

0

d)

DNE

34.

Find $\lim_{x\rightarrow-1^-\ }f\left(x\right)$

a)

4

b)

0

c)

-1

d)

DNE

35.

Find $\lim_{x\rightarrow-1^+\ }f\left(x\right)$

a)

4

b)

0

c)

-1

d)

DNE

36.

Find $\lim_{x\rightarrow-1\ }f\left(x\right)$

a)

4

b)

0

c)

-1

d)

DNE

37.

Find $\lim_{x\rightarrow-4^-\ }f\left(x\right)$

a)

-2

b)

3

c)

-4

d)

DNE

38.

Find $\lim_{x\rightarrow-4^+\ }f\left(x\right)$

a)

-2

b)

3

c)

-4

d)

DNE

39.

Find $\lim_{x\rightarrow-4\ }f\left(x\right)$

a)

-2

b)

3

c)

-4

d)

DNE

40.

Find $f\left(-4\right)$

a)

-2

b)

3

c)

-4

d)

undefined

41.

Find $f\left(4\right)$

a)

2

b)

4

c)

-4

d)

undefined

42.

Find $\lim_{x\rightarrow4\ }f\left(x\right)$

a)

2

b)

0

c)

-4

d)

DNE

43.

What is the limit?

a)

2

b)

-2

c)

1/2

d)

-1/2

44.

a)

0

b)

∞

c)

- ∞

d)

DNE

45.

What is the limit?

a)

DNE

b)

Infinity

c)

6

d)

12

46.

Derivative means the same thing as

a)

slope of the tangent line

b)

slope of the normal line

c)

exponent

d)

slope of the secant line

47.

Find the derivative of the given equation $x^3+x^2+12$

a)

$3x^2+2x$

b)

$5x$

c)

$3x^3+2x^2$

d)

$x^2+x$

48.

At which point(s) will the slope(s) of the tangent line be POSITIVE?

a)

at C only

b)

at points A, C and E only

c)

at point B and D only

d)

at points A and E only

49.

Find the fully simplified Derivative of y = 4x² + 3x + 6x^-2

a)

y' = 8x + 3 -12x^-3

b)

y' = 8x + 3 +12/x³

c)

y' = 8x + 3 -12/x³

d)

y' = 8x + 3 + 12/x

50.

At which point(s) will the slopes of the tangent line be zero?

a)

at C only

b)

at points A, C and E only

c)

at point B and D only

d)

at points A and E only

51.

Differentiate $f\left(x\right)=\frac{2}{x^5}-5$

a)

$-\frac{5}{x^4}$

b)

$-\frac{10}{x^4}$

c)

$\frac{2}{x^6}$

d)

$-\frac{10}{x^6}$

52.

Find the slope of $y=3x^2-5\ at\ x=2$

a)

10

b)

11

c)

12

d)

13

53.

Find the derivative of the function: $f\left(x\right)=\frac{1}{\sqrt{x^3}}$

a)

$f'\left(x\right)=-\frac{3}{2\sqrt{x^5}}$

b)

$f'\left(x\right)=-\frac{2}{3\sqrt{x^5}}$

c)

$f'\left(x\right)=-\frac{3}{\sqrt{x}}$

d)

$f'\left(x\right)=-\frac{3}{2\sqrt{x}}$

54.

Between which time intervals does the object speed up/increase velocity?(velocity moves away from 0 m/s point)

a)

0-10 sec and 40-55 sec

b)

15-30 sec and 40-55 sec

c)

0-10 sec and 30-40 sec

d)

15-30 sec and 30-40 sec

55.

Between which time intervals does the object slow down/decrease velocity?(velocity move towards 0 m/s point)

a)

0-10 sec and 40-55 sec

b)

15-30 sec and 40-55 sec

c)

0-10 sec and 30-40 sec

d)

15-30 sec and 30-40 sec

56.

How many times does this object have no acceleration?(no acceleration means velocity doesn't change so acceleration = 0 m/s²)

a)

0

b)

1

c)

2

d)

3

57.

What is the rate of acceleration during the first line segment? (slope between 0 - 10 sec)

a)

0 m/s²

b)

2.7 m/s²

c)

6 m/s²

d)

- 4 m/s²

58.

What is the rate of acceleration during the 2nd line segment? (slope between 10 - 15 sec)

a)

0 m/s²

b)

2.7 m/s²

c)

6 m/s²

d)

- 4 m/s²

59.

What is the rate of acceleration during the 3rd line segment? (slope between 15 - 40 sec)

a)

0 m/s²

b)

2.7 m/s²

c)

6 m/s²

d)

- 4 m/s²

60.

Calculate the average rate of change from 20 to 40 minutes.

a)

-2 minutes per gallon

b)

-20 minutes per gallon

c)

-2 gallons per minute

d)

-20 gallons per minute

61.

Average Rate of Change is also known as...

a)

y-intercept

b)

x-intercept

c)

linear

d)

slope

62.

Find the absolute extrema for f(x) = 2x³ + 6x² + 4 over the interval [-4, 0] (using calculus).

a)

Abs max @ (2, 12), Abs min @ (0, 4)

b)

Abs max @ (-4, 48), Abs min @ (0, 4)

c)

Abs max @ (2, 72), Abs min @ (0, 0)

d)

Abs max @ (2, 12), Abs min @ (-4, -28)

63.

A particle's speed is decreasing if

a)

it's acceleration is positive

b)

it's velocity is positive

c)

it's velocity and acceleration have the same sign

d)

it's velocity and acceleration have different signs

64.

What are the intervals of the graph increasing for f(x) = 2x⁴- 4x² + 1

a)

(-1,0)

b)

(0,1)

c)

(-∞,-1) $\cup$ (1,∞)

d)

(-1, 0) $\cup$ (1, $\infty$ )

65.

Which one of the following statements is always true?

a)

When a graph is increasing, its derivative is negative.

b)

When a graph is decreasing, so is its derivative.

c)

When a graph is decreasing, its derivative is negative.

d)

When a graph is increasing, so is its derivative.

66.

f(x) is a polynomial function. Which one of the following statements is FALSE?

a)

f(x) has a derivative of zero when the graph of f has a relative min or max.

b)

If the derivative of f(x) changes from positive to negative at some point, then the graph of f has a relative minimum at that point.

c)

If the derivative of f(x) is always positive, then the graph of f has no relative extrema.

d)

If the graph of f is always increasing, then the derivative of f(x) is never negative.

67.

If given f'(x) how would you find the intervals which the graph f(x) has a positive slope( increasing)?

a)

f'(x) < 0 (negative)

b)

f'(x) > 0 (positive)

c)

f'(x) is increasing

d)

Can't be determined

68.

When f'(x) changes from positive to negative, there is(are) ...

a)

a maximum.

b)

a minimum.

c)

no extrema.

On Ramps Unit 5 Precalc Review

Total questions: 68

Worksheet time: 3hrs 16mins

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