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Do all problems. (Show work for non multiple choice problems. If multiple choice, no need to show work.)

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Math 2

Midterm 1

Score :

/ 100

F 2020

Last Name :

First Name :

Multiple choice questions – write answer (A,B,C,…) in the answer blank provided. No need to show

work for multiple choice questions.

For all other questions, work must be shown neatly. No work = no credit. Circle/Box your answers. Write

your answer in the answer blank if appropriate. Use scratch paper if necessary but work on scratch

paper will not be graded. Scientific calculator OK. No graphing calculators.

Do not approximate unless asked to do so.

Solve the problem.

1) Find all points having an x-coordinate of 5 whose distance from the point (1, -2) is 8.

1)

Find an equation for the line with the given properties.

2) Containing the points (-7, 2) and (6, -2); Write answer in slope-intercept form

2)

1

Find the midpoint of the line segment joining the points P1 and P2 .

3) P1 = (y, 5); P2 = (0, 4)

A) y, 9

3)

B) y,

9

2

C)

y 9

,

2 2

Find the center (h, k) and radius r of the circle. Graph the circle.

4) x2 + y2 – 10x – 2y + 10 = 0

D) –

y

,1

2

4)

Center :

Radius:

Find the domain. Write answer in interval notation.

5) y = 36 – x2

5)

Find an equation for the line with the given properties.

6) Perpendicular to the line -7x + 4y = 52; containing the point (-4, 12)

A) 4x + 7y = 68

B) 4x – 7y = 52

C) 4x – 7y = 68

2

D) -7x – 4y = 68

6)

Solve the problem.

7) The profit that the vendor makes per day by selling x pretzels is given by the function

P(x) = -0.004×2 + 2.8x – 150. Find the number of pretzels that must be sold to maximize profit.

A) 350 pretzels

B) 1.4 pretzels

C) 700 pretzels

Find and simplify the average rate of change/difference quotient of f,

9) f(x) =

D) 340 pretzels

f(x) – f(1)

x-1

8) f(x) = 2×2 + 9x

Find and simplify the difference quotient of f,

7)

8)

f(x + h) – f(x)

, h 0, for the function.

h

5

x

9)

3

Solve the problem.

10) If a rocket is propelled upward from ground level, its height in meters after t seconds is given by

h = -9.8t 2 + 117.6t. During what interval of time will the rocket be higher than 343 m?

A) 0 < t < 5
B) 5 < t < 7
C) 10 < t < 12
10)
D) 7 < t < 10
11) A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions
10 inches by 22 inches by cutting out equal squares of side x at each corner and then folding up the
sides as in the figure. Express the volume V of the box as a function of x.
11)
22
10
A) V(x) = x(10 - 2x)(22 - 2x)
C) V(x) = (10 - x)(22 - x)
B) V(x) = x(10 - x)(22 - x)
D) V(x) = (10 - 2x)(22 - 2x)
Use the graph to find the intervals on which it is increasing, decreasing, or constant.
12)
A) Decreasing on - , -
2
and
2
,
; increasing on -
12)
,
2 2
B) Increasing on (- , )
C) Decreasing on - , 0 ; increasing on 0,
D) Increasing on - , -
2
and
2
,
; decreasing on -
,
2 2
Find the equation of the oblique asymptote, if any, of the function.
2x3 + 11x2 + 5x - 1
.
13) f(x) =
x2 + 6x + 5
A) y = 2x + 1
B) y = 0
C) y = 2x
4
13)
D) y = 2x - 1
For the given functions f and g, find the composite function.
Find (f g)(x).
14) f(x) = x2 + 5, g(x) = x 2 - 6;
A) x4 + 19
B) x4 + 41
C) x4 + 10x 2 + 19
Determine algebraically whether the function is even, odd, or neither.
What kind of symmetry does it have?
-x 3
15) f(x) =
3x2 - 2
D) x4 - 12x2 + 41
14)
15)
Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting. State the transformations clearly.
16) f(x) = 3 - x-1
16)
List the transformations clearly in the order they are to be performed:
1)
2)
3)
5
Solve the inequality. Write answer in interval notation.
17) x3 - 8x2 - 9x > 0

17)

Solve the inequality. Write answer in interval notation.

16x

4x

18)

7-x

18)

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f.

19) Degree 6; zeros: -3, 4, 3 – 5i, -4 + i

19)

6

Find the vertical asymptotes of the rational function.

x-3

20) f(x) =

9x – x3

20)

A) x = 0, x = -3, x = 3

C) x = -3, x = 3

B) x = 0, x = -3

D) x = 0, x = 3

Find the equation of the horizontal asymptote, if any, of the function.

8x – 4

21) h(x) =

x-4

A) y = 8

C) x = 4

B) y = 0

D) no horizontal asymptotes

Use the given zero to find the remaining zeros of the function.

22) f(x) = x3 + 4×2 – 10x + 12; zero: 1 + i

A) -6, 6

21)

B) 1 – i, 6i

Find all zeros of the function. Factor f(x).

23) f(x) = x4 + 6×3 + 17x 2 + 54x + 72

C) 1 – i, 6

22)

D) 1 – i, -6

23)

Zeros are :

Factored form :

7

Analyze the graph of the given function f as follows:

(a) Determine the end behavior:.

(b) Find the x- and y-intercepts of the graph.

(c) Determine whether the graph crosses or touches the x-axis at each x-intercept.

(d) Determine the max number of turning points

(e) Use the information obtained to draw the graph. Label all points clearly.

24) f(x) = -x 2 (x – 3)(x + 1)

24)

8

Analyze the function and sketch:

a) Find the domain in interval notation

b) Find all asymptotes : vertical, horizontal, oblique if any

c) Find the x and y intercepts

d) Determine whether the graph touches or crosses at each x intercept

e) Does the graph cross/intersect any of its asymptotes? If yes, where ?

f) Chart of signs using test points

g) Use the info from the steps a-f to sketch the graph.

x

25) f(x) =

x2 – 1

9

25)

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Tags:

slope intercept form

interval notation

graphing calculators

scientific calculator

the equation of the circle

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