Question

solve each of the problems below. be sure to ask questions if you need more help with a topic.
i can identify functions.

1. does the set of ordered pairs represent a function? explain.

{(6, -6), (7, -6), (8, -6), (9, -6)}

1. does the table represent a function? explain.

x	-3	-2	0	-3	-2
y	9	4	0	-9	-4

1. does the graph represent a function? explain.

(graph of a v - shaped graph with vertex at the origin, opening to the right and down)

1. does the graph represent a function? explain.

(graph of a curve starting at the origin and curving upwards to the right)

1. does the mapping represent a function? explain.

(mapping diagram with x - set: 7, 8, 9; y - set: -7, -8, -9. 7 maps to -7, 8 maps to -8, -9; 9 maps to -7, -8, -9)

1. does the set of ordered pairs represent a function? explain.

{(0, 5), (-2, -1), (0, -5), (3, 20)}
i can identify functions as linear or non - linear.

1. does the table below represent a linear function? why or why not?

x	-2	0	2	4
y	0.2	2	3.8	5.6

1. does the graph represent a linear relationship? explain.

(graph of a curve starting at the origin and curving upwards, getting less steep as x increases)

Explanation:

Step1: Check 1st ordered pairs

A function has unique x-values. All x-values (6,7,8,9) are unique.

Step2: Check 2nd table x-values

x-values: -3,-2,0,-3,-2. -3 and -2 repeat.

Step3: Check 3rd graph (Vertical Line Test)

A vertical line intersects 2+ points.

Step4: Check 4th graph (Vertical Line Test)

Any vertical line intersects at most 1 point.

Step5: Check 5th mapping x-values

Each x (7,8,9) maps to 1 y-value.

Step6: Check 6th ordered pairs

x-values: 0,-2,0,3. 0 repeats.

Step7: Check 7th table rate of change

Calculate $\Delta y/\Delta x$:
$\frac{2-0.2}{0-(-2)}=\frac{1.8}{2}=0.9$; $\frac{3.8-2}{2-0}=\frac{1.8}{2}=0.9$; $\frac{5.6-3.8}{4-2}=\frac{1.8}{2}=0.9$
Constant rate of change.

Step8: Check 8th graph linearity

Graph is a curve, not straight line.

Answer:

1. Yes; all x-values are unique.
2. No; x-values -3 and -2 repeat (one x maps to two y-values).
3. No; fails Vertical Line Test (a vertical line intersects multiple points).
4. Yes; passes Vertical Line Test (each x has one y).
5. Yes; each x maps to exactly one y-value.
6. No; x-value 0 repeats (maps to 5 and -5).
7. Yes; constant rate of change ($\frac{\Delta y}{\Delta x}=0.9$) between all points.
8. No; the graph is a curved line, not straight.