A. Function 1 has a greater rate of change than function 2.
C. Function 1 has a greater y-intercept than function 2.
Step-by-step explanation:
The rate of change of the function f(x) is
![\dfrac{f(b)-f(a)}{b-a}](/tpl/images/0422/7438/5bdb9.png)
Note that both functions are linear functions. The straight line represents the linear function and the table represents the linear function because ![\frac{11-5}{2-0}=\frac{20-11}{5-2}=\frac{29-20}{8-5}=3](/tpl/images/0422/7438/cb710.png)
Function 1:
![a=0\Rightarrow f(a)=5\\ \\b=2\Rightarrow f(b)=11](/tpl/images/0422/7438/5f8a0.png)
Rate of change
![\dfrac{11-5}{2-0}=\dfrac{6}{2}=3](/tpl/images/0422/7438/0a0e7.png)
Equation of function:
![y-5=3(x-0)\\ \\y=3x+5](/tpl/images/0422/7438/049de.png)
y-intercept:
![x=0\Rightarrow y=3\cdot 0+5=5](/tpl/images/0422/7438/9383f.png)
Function 2:
![a=0\Rightarrow f(a)=-1\\ \\b=2\Rightarrow f(b)=0](/tpl/images/0422/7438/58481.png)
Rate of change
![\dfrac{0-(-1)}{2-0}=\dfrac{1}{2}=0.5](/tpl/images/0422/7438/6a527.png)
Equation of function:
![y-(-1)=0.5(x-0)\\ \\y=0.5x-1](/tpl/images/0422/7438/f3720.png)
y-intercept:
![x=0\Rightarrow y=0.5\cdot 0-1=-1](/tpl/images/0422/7438/116a3.png)
A. Function 1 has a greater rate of change than function 2.
C. Function 1 has a greater y-intercept than function 2.