Answer:
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
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
Note that both functions are linear functions. The straight line represents the linear function and the table represents the linear function because [tex]\frac{11-5}{2-0}=\frac{20-11}{5-2}=\frac{29-20}{8-5}=3[/tex]
Function 1:
[tex]a=0\Rightarrow f(a)=5\\ \\b=2\Rightarrow f(b)=11[/tex]
Rate of change
[tex]\dfrac{11-5}{2-0}=\dfrac{6}{2}=3[/tex]
Equation of function:
[tex]y-5=3(x-0)\\ \\y=3x+5[/tex]
y-intercept:
[tex]x=0\Rightarrow y=3\cdot 0+5=5[/tex]
Function 2:
[tex]a=0\Rightarrow f(a)=-1\\ \\b=2\Rightarrow f(b)=0[/tex]
Rate of change
[tex]\dfrac{0-(-1)}{2-0}=\dfrac{1}{2}=0.5[/tex]
Equation of function:
[tex]y-(-1)=0.5(x-0)\\ \\y=0.5x-1[/tex]
y-intercept:
[tex]x=0\Rightarrow y=0.5\cdot 0-1=-1[/tex]
A. Function 1 has a greater rate of change than function 2.
C. Function 1 has a greater y-intercept than function 2.