sketch graphs Q2

Question

1. Sketch the graph of y=tan x ; 0degrees is less than and equal X less than and equal 360 degrees. 1.1. Skecth the graph of y = - x^2 + 5x - 4 1.1.1. Is the graph of y = - x^2 + 5x - 4 continuous or discontinuous? 1.2. Skecth and indicate the area enclosed by the graph y=3x - x^2 and the x-axis. Also, indicate the representative strip to be used to calculate the value of the enclosed area. 1.2.1. Calculate using integration, the value of the enclosed area above.

Answer 1

The function y = tan(x) and its graph in the interval [0, 360] is

Answer 2

(1.1).

The equation is y = - x² + 5x - 4.

Make the table of values to find ordered pairs that satisfy the equation.

Choose values for x and find the corresponding values for y.

x	y = - x2 + 5x - 4	(x, y)
- 1	y = - (-1)2 + 5(-1) - 4 = -10	(- 1, -10)
0	y = - (0)2 + 5(0) - 4 = - 4	(0, -4)
1	y = - (1)2 + 5(1) - 4 = 0	(1, 0)
2	y = - (2)2 + 5(2) - 4 = 2	(2, 2)
3	y = - (3)2 + 5(3) - 4 = 2	(3, 2)
4	y = - (4)2 + 5(4) - 4 = 0	(4, 0)
5	y = - (5)2 + 5(5) - 4 = - 4	(5, - 4)
6	y = - (6)2 + 5(6) - 4 = - 10	(6, - 10)

Graph :

Yes, the graph is continuous.

Since the polynomial functions are continuous at every point in their domain.

Answer 3

(1.2).

The equation is y = 3x - x² and the x-axis (y = 0).

Substitute y = 0 in the equation y = 3x - x².

3x - x² = 0

x(3 - x) = 0

x = 0 and x = 3.

Graph :

1.2.1.