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for the given functions f and g,

0 votes
(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
asked Jan 19, 2015 in PRECALCULUS by anonymous

4 Answers

0 votes

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:

graph the line equations f(x) = -2x-1 and g(x) = x^2-9.

answered Jan 19, 2015 by david Expert
edited Jan 19, 2015 by bradely
0 votes

(b)

Step 1:

The functions are and ..

Step 2:

Solve the equation  by factorization.    

    

or

  or                               

Step 3:

Substitute the  values in linear function.

image

image

image

image

Solution :

The solutions are image and image.

answered Jan 19, 2015 by david Expert
0 votes

(c) The functions are and .

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

Locate the points on the graph image and image.

Graph:

graph the line equations f(x) = -2x-1 and g(x) = x^2-9 by finding x values.

answered Jan 19, 2015 by david Expert
0 votes

(d)

 The functions are and .

Shade the region below image and above image.

Graph :

graph the line equations f(x) = -2x-1 and g(x) = x^2-9 and shading the intersection..

answered Jan 19, 2015 by david Expert

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