Question

review module 6
1 use your vocabulary words to fill in the blanks.
a _____ is any set of ordered pairs. set set of paired inputs & outputs
a _____ of a function is the set of all possible input values.
c a function whose graph is not a straight line is _____
d the _____ of a function is the set of all possible output values.
e a function whose graph is a straight line is _____
f ___ is a linear equation written in the form ( y = mx + b ), where ( m ) represents the _ and the ( b ) represents the ___.
g. how do you find slope from a graph ___ and from a set of ordered pairs ___
h when asked to find the initial value you are looking for the ___ when asked to find the rate of change you are looking for the ___.

1. which relation is a function?

a ( {(-4, -8), (-2, -8), (6, -8)} )
b ( {(-4, 2), (-4, 6), (-2, 6)} )
c ( {(-8, -4), (-8, -2), (-8, 6)} )
d ( {(-8, 2), (6, -4), (6, -2)} )
3 a relation is shown in the graph. place an x in the table to show whether each statement is true or false.

	true	false
the domain is all real numbers.
the range includes negative real numbers.

4 which equation represents a linear function? solve each equation for y first!!
a ( 2xy + y = 9 )
b ( y = 12sqrt{x} - 5 )
c ( 3y + x^2 + x = 0 )
d ( 4x + 2(y - 1) = 0 )

Explanation:

Step1: Solve Q1 Vocabulary Blanks

A. Relation is any set of ordered pairs.
B. Domain of a function is the set of all possible input values.
C. A function whose graph is not a straight line is non-linear.
D. The range of a function is the set of all possible output values.
E. A function whose graph is a straight line is linear.
F. In $y=mx+b$, $m$ = slope, $b$ = y-intercept.
G. From a graph: use $\frac{\Delta y}{\Delta x}$; from ordered pairs: $\frac{y_2-y_1}{x_2-x_1}$
H. Initial value = y-intercept; rate of change = slope

Step2: Solve Q2 Function Check

A relation is a function if each input has one output.

• Option A: Inputs -4, -2, 6 repeat → Not a function
• Option B: All inputs (-4, -2) have unique outputs → Function
• Option C: Input -8 repeats → Not a function
• Option D: Input 6 repeats → Not a function

Step3: Solve Q3 Graph Relation Checks

From the graph:

1. The relation is a function: Passes vertical line test → True (X in True column)
2. Domain is all real numbers: Graph spans all x-values → True (X in True column)
3. Range includes negative real numbers: Graph goes below y=0 → True (X in True column)

Step4: Solve Q4 Linear Function Check

Linear functions have form $y=mx+b$ (no exponents/roots on x):

• A: $2xy+y=9 \implies y=\frac{9}{2x+1}$ → Non-linear
• B: $y=12\sqrt{x}-5$ → Non-linear (square root)
• C: $3y+x^2+x=0 \implies y=\frac{-x^2-x}{3}$ → Non-linear (x² term)
• D: $4x+2(y-1)=0 \implies 4x+2y-2=0 \implies y=-2x+1$ → Linear

Each input has exactly one output.

3.

Statement	True	False
The domain is all real numbers.	X
The range includes negative real numbers.	X

1. D. $4x + 2(y - 1) = 0$

Answer:

1.
A. Relation
B. Domain
C. non-linear
D. Range
E. linear
F. slope; y-intercept
G. Use vertical change over horizontal change; Use $\frac{y_2-y_1}{x_2-x_1}$
H. y-intercept; slope

1. B. [(-4, 2), (-4, 6), (-2, 6)]