Math Chapter 2 Exercises

1. Plot the following points on the co-ordinate axis:
(a) (2, 3)
(b) (-2, 3)
(c) (2,-3)
(d) (0, 3)
(e) (-2, 0)
(f) (-5,-3, )

2. Compute several points that lie on the graph of the fol lowing functions
and use these points to sketch their graphs.
(a) f(x) = 1 - x
(b) f(x) = |x| + 1
(c) f(x) = x²
(d) f(x) =

For problems 3 and 4 let g(x) = -x, h(x) = 2x, j(x) = x+2,
k(x) = x - 1 and f any other function.

3. Compute the following compositions in terms of the function f, for
example (f ◦ k)(x) = f(k(x)) = f(x - 1) and (j ◦ f)(x) = j(f(x)) =
f(x) + 2.
(a) (g ◦ f)(x)
(b) (h ◦ f)(x)
(c) (f ◦ j)(x)
(d) (k ◦ f)(x)
(e) (k ◦ (g ◦ (f ◦ j)))(x)

4. For the graph shown of a given function f. Sketch the graphs of
• (g ◦ f)(x)
• (h ◦ f)(x)
• (f ◦ j)(x)
• (k ◦ f)(x)
• (k ◦ (g ◦ (f ◦ j)))(x)

5. Which of the following functions are continuous?
(a) f(x) = |xj|
(b) f(x) = [x]
(c) f(x) = x

6. Sketch the graph of the relation {(x, y)|x + y² = 1} (hint: pick values
for y and solve for x , i.e. let y = -3,-2,-1, 0, 1, 2, 3 and find the
corresponding values for x .

7. Write the equation of a circle with radius 2 whose center is (1,-1).

8. Find the center and radius of a circle whose equation is given by
x² + 4x + y² - 6y = -4, and draw the graph of the circle.

9. Find the center and radius of a circle whose equation is given by
x² + 2x + y² - 3 = 0, and draw the graph of the circle.

10. Let and g(x) = |x|, draw the graphs of
(a) f ◦ g
(b) g ◦ f
(c) f + g