Sketch two different examples of functions for each that would satisfy the following
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
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)
a) To satisfy the conditions for function f:
Example 1:
Let f(x) = 2x - 6
Graph:
- For x = 0, f(0) = 2(0) - 6 = -6
- For x = 3, f(3) = 2(3) - 6 = 0
- For x = -4, f(-4) = 2(-4) - 6 = -14
Example 2:
Let f(x) = x^2 - 5x + 6
Graph:
- For x = 0, f(0) = (0)^2 - 5(0) + 6 = 6
- For x = 3, f(3) = (3)^2 - 5(3) + 6 = -2
- For x = -4, f(-4) = (-4)^2 - 5(-4) + 6 = 1
b) To satisfy the conditions for function g:
Example 1:
Let g(x) = 3x + 15
Graph:
- For x = -5, g(-5) = 3(-5) + 15 = 0
- For x = -2, g(-2) = 3(-2) + 15 = 0
- For x = 3, g(3) = 3(3) + 15 = 24
Example 2:
Let g(x) = -2x^2 + 4x
Graph:
- For x = -5, g(-5) = -2(-5)^2 + 4(-5) = 0
- For x = -2, g(-2) = -2(-2)^2 + 4(-2) = 0
- For x = 3, g(3) = -2(3)^2 + 4(3) = 7