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

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

$\dfrac{f(b)-f(a)}{b-a}$

Note that both functions are linear functions. The straight line represents the linear function and the table represents the linear function because $\frac{11-5}{2-0}=\frac{20-11}{5-2}=\frac{29-20}{8-5}=3$

Function 1:

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

Rate of change

$\dfrac{11-5}{2-0}=\dfrac{6}{2}=3$

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

$\dfrac{0-(-1)}{2-0}=\dfrac{1}{2}=0.5$

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.