M121 Fall 95  Exam I  Sept. 15, 1995

Name (Print) SSN: Circle the name of your TA and Discussion Hour:

David Krebes  9 AM  11 AM
Qihui Liu:  8am  9am
Jukun Ying  9am  11 am

M121 Fall 95  Exam I  Sept. 15, 1995

Answer all questions and SHOW ALL WORK. No credit for answers only.

Part I: Multiple choice. No partial credit but SHOW WORK! Circle the letter corresponding to

the correct answer.

1. A correct expression for the distance between the two points (x, 5) and (3, 9) is:

(A) \sqrt{(x − 5)^{2} + (3 − 9)^{2}}
(B) \sqrt{x^{2} − 5^{2} + 3^{2} − 9^{2}}
(C) \sqrt{x^{2} − 6x + 25}

(D) |x − 5| + |3 − 9| (E) (x − 3)^{2} + (9 − 5)^{2}

2. If sec θ = 13/5 and 3π/2 < θ < 2π, what is sin(θ)? (A) 5/13 (B) 12/13 (C) −12/13 (D) −13/5 (E) 67.38^{o}

M121 Fall 95  Exam I  Sept. 15, 1995

3. What is the period of tan(π/2 − x)? (A) π/2 (B) 2π (C) π (D) π/4 (E) 3 4. Determine f(x) ∘ g(x) if f(x) = (2x − 3)/4 and g(x) = x^{2} − 2. (Remember: f ∘ g means

”Do g first”.)

(A) (2x^{2} − 7)/4

(B) (4x^{2} − 12x − 23)/16

(C) (2x^{3} − 6x^{2} − 4x + 6)/4

(D) (x^{2} + 2x − 5)/4

(E) (2x^{2} − 3)/4

5. Determine g(x) ∘ f(x) if f(x) = (2x − 3)/4 and g(x) = x^{2} − 2.

(A) (2x^{2} − 7/4

(B) (4x^{2} − 12x − 23)/16

(C) (2x^{3} − 6x^{2} − 4x + 6)/4

(D) (x^{2} + 2x − 5)/4

(E) (2x^{2} − 3)/4

M121 Fall 95  Exam I  Sept. 15, 1995

6. A car whose tires have a diameter of 16 inches is pushed 10 feet down the driveway. How many times does each wheel rotate?

(A) 7.48 (B) 856.8 (C) 2.39 (D) 120 inches (E) 160 inches

7. The graph of y = x^{2} is transformed in the following order:

1. stretch VERTICALLY by a factor of 3 2. shift RIGHT by 0.8 units

3. shift UP by 1.3 units The resulting graph is the graph of the function

(A) y = (3x − 0.8)^{2} + 1.3 (B) y = 3(x − 0.8)^{2} + 1.3 (C) y = 3(x + .8)^{2} + 3.9 (D) y = 3(x − 0.8)^{2} + 3.9 (E) y = (3x + 1.6)^{2}

M121 Fall 95  Exam I  Sept. 15, 1995

Part II : (Partial credit) Write complete solutions and indicate your answers clearly.

8. Consider the function f(x) = 15 sec x. (The calculator may not be helpful for the first four parts of this problem.) Give the domain: . Give the range: . Give the period: . Describe all vertical asymptotes: . Sketch the graph for x in the interval [0, 2π]. Be sure to label the coordinates of all xintercepts and all y-intercepts. Draw and label all vertical asymptotes using a dotted line. Clearly indicate the scale on each axis.

9. The angle of elevation of the top of a building from a point 50m away from the building is 58^{∘}. Determine the building’s height.

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10. Among the rectangles with perimeter 100 find the length and width of the one with the maximum area.

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11. Let

f(x) = \{ \begin{matrix}−x, & if 0 ≤ x < 5 \\ \sqrt{x − 4}, & if x ≥ 5. \end{matrix}

What is the domain of f?

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What is the range of f?

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Sketch a complete graph of this function.

M121 Fall 95  Exam I  Sept. 15, 1995

12. The function f(x) in the following graph is periodic with period less than 4π. What is the period of the function?

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What is its domain?

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What is the maximum value of f?

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What is the minimum value of f?

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What is its amplitude?

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What is a function that could have this graph?

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