Sketch two different examples of functions for each that would satisfy the following

Question

conditions. (i.e. make two different graphs for (a) and two for (b))
a) f(0)=6, f(3)=-2, f(-4)=1

b) g(-5), g(-2)=0, g(3)=7

Answer 1

a) Two different examples of functions that satisfy the given conditions are:

Example 1:
f(x) = -x + 6
Graph for Example 1:
- The graph starts at (0,6)
- The graph passes through the point (3,-2)
- The graph passes through the point (-4,1)

Example 2:
f(x) = -0.5x + 4.5
Graph for Example 2:
- The graph starts at (0,4.5)
- The graph passes through the point (3,-2)
- The graph passes through the point (-4,1)

b) Two different examples of functions that satisfy the given conditions are:

Example 1:
g(x) = 2x - 10
Graph for Example 1:
- The graph passes through the point (-5,0)
- The graph passes through the point (-2,0)
- The graph passes through the point (3,7)

Example 2:
g(x) = 3x - 15
Graph for Example 2:
- The graph passes through the point (-5,0)
- The graph passes through the point (-2,0)
- The graph passes through the point (3,7)