Assignment

1. Determine whether the function is odd, even, neither, or can't be determined:
h(x) = x² - x⁴
A. Even
B. Odd
C. Neither
D. Can't be determined

2. Write an equation in general form of the line passing through (3, -5) whose slope is the negative reciprocal (the reciprocal with the opposite sign) of -1/4.
A. 5x + y - 22 = 0
B. 4x - y - 17 = 0
C. 4x + y + 20 = 0
D. 7x - y + 34 = 0

3. Determine whether the following equation defines y as a function of x:
x + y = 16
A. Y is a function of x.
B. Y is not a function of x.
C. X is a function of y.
D. X is not a function of y.

4. Find the average rate of change of the function from x₁ to x₂.
f(x) = x² + 2x from x₁ = 3 to x₂ = 5
A. 10
B. 15
C. 4
D. 25

5. Determine whether the function is odd, even, neither, or can't be determined:
g(x) = x² + x
A. Even
B. Odd
C. Neither
D. Can't be determined

6. Give the slope and y-intercept of each line whose equation is given.
y = -3/5x + 7
A. m = 3/4; b = -2
B. m = 6; b = 7
C. m = -3/5; b = 7
D. m = 1; b = 8

7. Write an equation in slope-intercept form of a linear function f whose graph satisfies the given conditions.
The graph of f is perpendicular to the line whose equation is 3x - 2y - 4 = 0 and has the same y-intercept as this line.
A. f(x) = 2/3x - 4
B. f(x) = -2/5x - 6
C. f(x) = -2/3x - 2
D. f(x) = -2/7x + 8

8. Give the slope and y-intercept of each line whose equation is given.
g(x) = -1/2x
A. m = 3/4; b = -2
B. m = 6; b = 7
C. m = -1/2; b = 0
D. m = 1; b = 8

9. Give the slope and y-intercept of each line whose equation is given.
y = 2x + 1
A. m = 3; b = 4
B. m = 5; b = 1
C. m = 6; b = 7
D. m = 2; b = 1

10. Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical.
(4, -2) and (3, -2)
A. 1; rises
B. 4; fall
C. 0; horizontal
D. 0; vertical

11. Evaluate each function at the given values of the independent variable and simplify.
g(x) = x² + 2x + 3
1. g(-1)
2. g(x + 5)
3. g(-x)

A.
1. 2
2. x² + 12x + 38
3. x² - 2x + 3

B.
1. 4
2. x² + 6x + 38
3. x² - 3x +5

C.
1. 7
2. x² + 7x + 56
3. x²+ 4x + 7

D.
1. 5
2. x² -12x + 38
3. x²+ 5x + 7

12. Determine whether the following equation defines y as a function of x:
x² + y = 16
A. Y is not a function of x.
B. X is a function of y.
C. X is not a function of y.
D. Y is a function of x.

13. Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical.
(5, 3) and (5, -2)
A. 1; rises
B. 4/9;horizontal
C. Undefined; vertical
D. Undefined; falls

14. Find the average rate of change of the function from x₁ to x₂.
f(x) = 3x from x₁ = 0 to x₂ = 5
A. -4
B. 8
C. 2
D. 3

15. Determine whether the function is odd, even, neither, or can't be determined:
f(x) = x³ + x
A. Even
B. Odd
C. Neither
D. Can't be determined

16. Write an equation in slope-intercept form of a linear function f whose graph satisfies the given conditions.
The graph of f passes through (-1, 5) and is perpendicular to the line whose equation is x = 6.
A. f(x) = 6
B. f(x) = 8
C. f(x) = 3
D. f(x) = 5

17. Determine whether the following equation defines y as a function of x:
x² + y² = 16
A. Y is a function of x.
B. X is not a function of y.
C. X is a function of x.
D. Y is not a function of x.

18. Use the given conditions to write an equation for each line in general form.
Passing through (-2, 2) and parallel to the line whose equation is 2x - 3y - 7 = 0.
A. 3x - 3y + 11 = 0
B. 2x - 3y + 10 = 0
C. 6x - 4y + 12 = 0
D. 2x - 5y + 15 = 0

19. Evaluate each function at the given values of the independent variable and simplify.
f(x) = 4x + 5
1. f(6)
2. f(x + 1)
3. f(-x)

A. 1. 27
2.5x + 9
3. -4x + 8

B. 1. 35
2.4x + 9
3. -7x + 5

C. 1. 29
2.4x + 9
3. -4x + 5

D. 1. 29
2.3x + 8
3. 4x + 6

20. Use the given conditions to write an equation for each line in general form.
Passing through (4, -7) and perpendicular to the line whose equation is x - 2y - 3 = 0.
A. 6x - y - 1 = 0
B. 4x + y + 1 = 0
C. 7x - y + 2 = 0
D. 2x + y - 1 = 0.