Answer:
g and h
Step-by-step explanation:
both g and h have constant relationships while f's f(x) values aren't constant so it doesn't have a linear relationship
Answer:
Of the three functions g and h represent linear relationship.
Step-by-step explanation:
If a function has constant rate of change for all points, then the function is called a linear function.
If a lines passes through two points, then the slope of the line is
[tex]m=\frac{x_2-x_1}{y_2-y_1}[/tex]
The slope of function f(x) on [1,2] is
[tex]m_1=\frac{11-5}{2-1}=6[/tex]
The slope of function f(x) on [2,3] is
[tex]m_2=\frac{29-11}{3-2}=18\neq m_1[/tex]
Since f(x) has different slopes on different intervals, therefore f(x) does not represents a linear relationship.
From the given table of g(x) it is clear that the value of g(x) is increased by 8 units for every 2 units. So, the function g(x) has constant rate of change, i.e.,
[tex]m=\frac{8}{2}=4[/tex]
From the given table of h(x) it is clear that the value of h(x) is increased by 6.8 units for every 2 units. So, the function h(x) has constant rate of change, i.e.,
[tex]m=\frac{6.8}{2}=3.4[/tex]
Since the function g and h have constant rate of change, therefore g and h represent linear relationship.
