Question

quarter 2 final

1. is the relation shown below a

function? use the graph below to
justify your answer.
(0, 3), (1, 4), (2, 3), (3, 0), (5, 4)
graph of a coordinate plane with x from 0 to 9 and y from 0 to 9

1. consider the two functions below.

which one of these functions is
linear? what is its equation? enter
any answers to two decimal places.
function a
graph of a line on a coordinate plane with x from -4 to 4 and y from -2 to 4
function b

x	1	2	3	4	5
y	1	8	27	64	125

function ______ is linear.
its equation is y = ____x + ____.

1. which function has a greater rate

of change?
function a
y = 10x - 3
function b

x	1	2	3	4	5
y	20	15	10	5	0

function a has a rate of change of
______ and function b has a rate
of change of ______, so function
______ has a greater rate of change.

1. consider the two functions below.

which one of these functions is
linear? what is its equation? enter
any answers to two decimal places.
function a

x	3	6	9	12	15
y	5	10	15	20	25

function b
graph of a curve on a coordinate plane with x from 0 to 9 and y from 0 to 9
function ______ is linear.
its equation is y = ____x + ____.

Explanation:

Step1: Check function definition

A relation is a function if each input (x-value) maps to exactly one output (y-value). For the set \((0, 3), (1, 4), (2, 3), (3, 0), (5, 4)\), all x-values (0,1,2,3,5) are unique, so each has one y-value.

Step2: Identify linear function (Q2)

Linear functions have constant rate of change. Function A's graph is a straight line. Function B: \(y=x^3\) (non-linear, rate changes). Calculate slope of Function A: use points (0,0) and (2,2): \(\frac{2-0}{2-0}=1\), y-intercept is 0.

Step3: Calculate rates of change (Q3)

Function A: \(y=10x-3\) is in \(y=mx+b\), so rate \(m=10\). Function B: use \(\frac{y_2-y_1}{x_2-x_1}=\frac{15-20}{2-1}=-5\). Compare 10 and -5.

Step4: Identify linear function (Q4)

Function A: check rate of change: \(\frac{10-5}{6-3}=\frac{5}{3}\), \(\frac{15-10}{9-6}=\frac{5}{3}\) (constant). Function B's graph is curved (non-linear). Calculate y-intercept: use \(y=\frac{5}{3}x+b\), plug (3,5): \(5=\frac{5}{3}(3)+b \to 5=5+b \to b=0\).

Answer:

1. Yes, it is a function. Each x-value corresponds to exactly one y-value, satisfying the definition of a function.
2. Function A is linear.

Its equation is \(y = 1.00x + 0.00\)

1. Function A has a rate of change of 10 and Function B has a rate of change of -5, so Function A has a greater rate of change.
2. Function A is linear.

Its equation is \(y = 1.67x + 0.00\)