# Laurel Springs High School Calculus Problems Report

1.

Which of the following relations are functions? (2 points)

1. y = -x + 3
2. x = y + 3
3. x – y = 3
 None of them All of them Choice II only Choice III only

2.

Find the range for f(x) = x2 + 1, for x < 0. (2 points)

 y ≥ 1 y > 1 y < 1 y ≤ 1

3.

Find the domain for . (2 points)

 x ≠ 2 x ≠ -3 x ≠ -3, -2 x ≠ -2

4.

Find the range of the function: f(x) = x + 3, for x ≠ 1. (2 points)

 All real numbers y ≠ 4 y ≠ 3 y ≠ 1

5.

Determine whether f(x) = 5x2 + 3x + 4 has a maximum or minimum. (2 points)

 Maximum Minimum

6.

Where is the function 4(x + 2)(x – 3)3 > 0? (2 points)

 When x < -2 or x > 3 When x > -2 or x < 3 For no x values For all x values

7.

For which x value would the graph of y = x2 – 25 be below the x-axis? (2 points)

 7 6 5 4

8.

Find f(g(-3)) if and g(x) = (x – 1)2 . (2 points)

 18 32 1

9.

Find f[g(x)] if f(x) = x2 + 1 and g(x) = x3. (2 points)

 x6 + 1 x8 + 1 (x2 + 1)3 None of these

10.

Find g(x) if g(x) is the resulting function from moving f(x) = (x + 2) right 1 unit and up 6 units. (2 points)

 g(x) = (x + 1) + 6 g(x) = (x – 1) + 6 g(x) = (x + 3) + 6 g(x) = (x – 6) + 1

11.

Rewrite f(x) = sin(x) if the function is stretched vertically by a factor of 3. (2 points)

 sin(3x) 3sin(x)

12.

What is the domain of ? (2 points)

 All real numbers less than 3 All real numbers except 3 All real numbers greater than 1 All real numbers greater than 3 All real numbers

13.

Find the range of . (2 points)

 y > 3 y ≥ 3 y ≥ 0 All real numbers

14.

Is the function of even, odd, or neither? (2 points)

 Even Odd Neither

15.

Find the period and amplitude for f(x) = 3sin(2x). (2 points)

 Amplitude = 2, Period = . Amplitude = 3, Period = π Amplitude = , Period = 2π Amplitude = 3, Period =

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