Question

quiz: functions
for questions 1-2, determine whether the representation is a function by writing \yes\ or
o.\
1.

x	-2	-1	1	2
y	4	1	1	4

2.
graph of a relation with a point at the origin and two curves opening to the left

1. which is not a true statement about a linear function?

a. its graph must pass through the origin.
b. it must have a constant rate of change.
c. it can be written in the form of $y = mx + b$.
d. its graph will be a straight line.

1. the list of ordered pairs below represents a function. which of the following could be the missing ordered pair?

$\\{ (12, 6), (3, 1), (2, -2), (5, 10), (-8, -4), (\underline{quad}, \underline{quad}) \\}$
a. $(2, 1)$
b. $(12, 7)$
c. $(-8, 8)$
d. $(-3, -4)$

1. the graph of a linear relationship has a slope of -5 and passes through the point $(2, -12)$. write the equation of the line in slope-intercept form.

Explanation:

Step1: Check 1st table for function

A function has unique x-values. All x-values (-2, -1, 1, 2) are unique.

Step2: Check 2nd graph for function

Use vertical line test: A vertical line intersects the graph at 2 points, so x maps to 2 y-values.

Step3: Analyze linear function statements

Linear functions follow $y=mx+b$. They have constant slope, straight graph, but don't need to pass through origin (e.g., $y=x+1$).

Step4: Find valid missing function pair

A function needs unique x-values. Existing x-values: 12,3,2,5,-8. Option D has new x=-3.

Step5: Substitute into slope-intercept formula

Use point-slope form $y-y_1=m(x-x_1)$ with $m=-5$, $(x_1,y_1)=(2,-12)$:
$y-(-12)=-5(x-2)$
Simplify to slope-intercept: $y+12=-5x+10$ → $y=-5x-2$

Answer:

1. Yes
2. No
3. A. Its graph must pass through the origin.
4. D. (-3, -4)
5. $y=-5x-2$