Question

Two functions are represented in different formats.

Function 1:


x y

0 5

2 ​11​

5 ​20​

8 ​29​


Function 2:








Which statements are true?


Select each correct answer.



A. Function 1 has a greater rate of change than function 2.


B. Function 2 has a greater rate of change than function 1.


C. Function 1 has a greater y-intercept than function 2.


D. Function 2 has a greater y-intercept than function 1.

Answer 1

A. Function 1 has a greater rate of change than function 2.

C. Function 1 has a greater y-intercept than function 2.

Explanation:

The rate of change of the function f(x) is

`(f(b)-f(a))/(b-a)`

Note that both functions are linear functions. The straight line represents the linear function and the table represents the linear function because
`(11-5)/(2-0)=(20-11)/(5-2)=(29-20)/(8-5)=3`

Function 1:

`a=0\Rightarrow f(a)=5\\ \\b=2\Rightarrow f(b)=11`

Rate of change

`(11-5)/(2-0)=(6)/(2)=3`

Equation of function:

`y-5=3(x-0)\\ \\y=3x+5`

y-intercept:

`x=0\Rightarrow y=3\cdot 0+5=5`

Function 2:

`a=0\Rightarrow f(a)=-1\\ \\b=2\Rightarrow f(b)=0`

Rate of change

`(0-(-1))/(2-0)=(1)/(2)=0.5`

Equation of function:

`y-(-1)=0.5(x-0)\\ \\y=0.5x-1`

y-intercept:

`x=0\Rightarrow y=0.5\cdot 0-1=-1`

A. Function 1 has a greater rate of change than function 2.

C. Function 1 has a greater y-intercept than function 2.