MATHS HOMEWORK

MATHS HOMEWORK
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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