f(x) and g(x)

[nycmath]

Precalculus
Michael Sullivan
Edition 10
Chapter 1, Section 3.1

30. Suppose that f(x) = 3x + 5 and g(x) = -2x + 15.

A. Solve f(x) = 0

Set 3x + 5 = 0 and solve for x.

2x + 5 = 0

2x = - 5

x = -5/2

B. Solve f(x) < 0.

Set 3x + 5 < 0 and compute.

3x + 5 < 0

3x < - 5

x < -5/3

C. Solve f(x) = g(x).

Set 3x + 5 = -2x + 15 and solve for x.

3x + 5 = - 2x + 15

3x + 2x = 15 - 5

5x = 10

x = 10/5

x = 2

D. Solve f(x) [tex]\ge[/tex] g(x).

Set 3x + 5 [tex]\ge[/tex] -2x + 15 and compute.

3x + 5 [tex]\ge[/tex] - 2x + 15

3x + 2x [tex]\ge[/tex] 15 - 5

5x [tex]\ge[/tex] 10

x [tex]\ge[/tex] 10/5

x [tex]\ge[/tex] 2

E. Graph y = f(x) and y = g(x) and label the point that represents the solution to the equation f(x) = g(x).

Note: Part C above gave us x = 2.
If I let x be 2 for f(x) and g(x), the point representing the solution is (2, 11). The solution is where the two lines meet or cross.

You say?

See attachment.

[Eigenvalue]

Yes. This is correct. I noticed that you only listed two points in your tables for f(x) and g(x). While plotting two points may be helpful for a linear function, it may be helpful to plot at least five--2 with positive x-values, 2 with negative x-values, and one with x=0--for higher degree polynomials.