for the given functions f and g,

Question

(a) Graph f and g on the same Cartesian plane.
(b) Solve f(x) = g(x)
(c) Use the result of part (b) to label the points of intersection of the graphs of f and g.
(d) Shade the region for which f(x) > g(x) ,that is,the region below f and above g.

f(x) = 2x -1 and g(x) = x^2 -4

Answer 1

Step 1:

(a) The functions are and .

represents line and parabola in the graph.

To graph the two equations we need some points through the equations.

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

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

x	y = x 2 - 4	(x , y )
-2	y = (- 2)2 - 4	(-2, 0)
0	y = (0)2 - 4	(0, -4)
2	y = (2)2 - 4	(2, 0)

 

x	y = 2x - 1	(x , y )
-2	y = 2(-2) - 1	(-2, -5)
0	y = 2(0) - 1	(0, -1)
2	y = 2(2) - 1	(2, 3)

Step 2:

1. Draw a coordinate plane.

2. Plot the points found in tables and draw curve and line through these points.

Graph:

.

Answer 2

(b)

Step 1:

The functions are and ..

Step 2:

Solve the equation  by factorization.    

    

or

  or                               

Step 3:

Substitute the  values in linear function.

Solution :

The solutions are and .

Answer 3

(c) The functions are and .

From (b) the solutions are intersection points of and .

Locate the points on the graph and .

Graph:

Answer 4

(d)

 The functions are and .

Shade the region below and above .

Graph :

.