Calculus, 8th Edition,stewart; page 33 problem 8

Question

What do all members of the family of linear functions f(x) = 1 + m(x + 3) have in common? Sketch several members of the family.

Answer 1

Step:1

The function is .

The members of this family can be obtained by substituting different values for .

Substitute  in .

Equation of a line .

Substitute  in .

Equation of a line .

Substitute  in .

Equation of a line .

Substitute  in 

Equation of a line .

Step:2

Graph :

Graph the members of the family are , ,  and .

All members of this family are linear functions, which represents straight lines.

All these straight lines passing through the point .

Solution:

All these straight lines passing through the point .

Graph of the members of the family :

.