Question 1. For each of the following find f ? g, g ? f and their domains.

(a) f(x) = 1

x

2

, g(x) = v

x

(b) f(x) = 2x

x

2 + 1

, g(x) = 2 + v

x – 1

(c) f(x) = x

2 + x

4 – 4x

3

, g(x) = x + 1

(d) f(x) = 1

x

2

, g(x) =

v

x – 1

x

2

(e) f(x) = 1

x

, g(x) = 1

x

2

Question 2. Compute the following:

(a) (f ? g)(4) where f(x) = 1

x

2

, g(x) = v

x

(b) (f ? g)(5) where f(x) = 2x

x

2 + 1

, g(x) = 2 + v

x – 1

(c) (f ? g)(-1) where f(x) = x

2 + x

4 – 4x

3

, g(x) = x + 1

Question 3. Find the equations of the following lines (express them in the general linear form).

(a) The line that passes through (-1, 7) and has slope -5

(b) The line that passes through (-6, 1) and (1, 4)

(c) The line that has slope 2 and y-intercept 4.

(d) The line that is horizontal and passes through (-2, -5).

(e) The line that is vertical and passes through (2, -3).

Question 4. Find the equation of the line in slope-intercept form.

(a) The line passing through (2, 3) and parallel to y = 4x + 3.

(b) The line passing through (2, 1) and parallel to y = 2.

(c) The line passing through (-7, -5) and parallel to 2x + 3y + 6 = 0.

(d) The line passing through (-4, -5) and perpendicular to the line 3y =

-2x

5

+ 3.

(e) The line passing through (1, 1) and (3, 3).

(f) The line parallel to x = -4 and passing through (2, -8)

(g) The line perpendicular to 3x + 2y – 4 = 0 and through (3, 4).

Question 5. Find the slope and the y-intercept of the following lines.

(a) y = 4x – 6

(b) x + 9 = 2

(c) y + 4 = 7

(d) x – 9 = 5y + 3

1

2 MTH121 HOMEWORK 2

(e) y – 7 = 3(x – 4)

Question 6. Determine if the following lines are parallel , perpendicular or neither.

(a) y = -5x + 7 and y = -5x – 3

(b) y = 4x + 3 and y = 5 + 4x

(c) y = x and y = -x

(d) y = 3 and x =

-1

3

(e) x – 2 = 3 and y = 2

Question 7. Graph the following functions.

(a) f(x) = 3x – 1

(b) f(x) = -2x + 2

(c) f(x) = 9x

2

(d) f(x) = x

2 – 4

(e) f(x) = 2x

2 + 3x – 2

(f) f(x) = 1 – x – x

2

(g) f(x) = x

2 + 6x + 11

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