Question

date 02/06 period
identify the domain and range of the function. use a mapping diagram to determine whether the relation is a function.

1. {(6, -7), (5, -8), (1, 4), (7, 5)}

solve the equation if the domain is {-2, -1, 0, 1, 2}. find the range and write the answers as ordered pairs.

1. $y=2x - 7$

use the table to the right to solve questions 3 and 4.

1. is the relationship a linear function?
2. what is the equation that describes the relationship?

1. graph the set of ordered pairs (1,2), (2,4), (3,6), (4, 8). determine whether the relationship is a linear function.

Explanation:

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Problem 1

Step1: Identify domain (x-values)

Domain: $\{1, 5, 6, 7\}$

Step2: Identify range (y-values)

Range: $\{-8, -7, 4, 5\}$

Step3: Check if it's a function

Each x maps to one y: Yes, it is a function.

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Problem 2

Step1: Substitute $x=-2$

$y=2(-2)-7=-4-7=-11$; Pair: $(-2,-11)$

Step2: Substitute $x=-1$

$y=2(-1)-7=-2-7=-9$; Pair: $(-1,-9)$

Step3: Substitute $x=0$

$y=2(0)-7=0-7=-7$; Pair: $(0,-7)$

Step4: Substitute $x=1$

$y=2(1)-7=2-7=-5$; Pair: $(1,-5)$

Step5: Substitute $x=2$

$y=2(2)-7=4-7=-3$; Pair: $(2,-3)$

Step6: Identify range

Range: $\{-11, -9, -7, -5, -3\}$

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Problem 3

Step1: Check constant rate of change

$\Delta x = 1-0=1$, $\Delta y=7-6=1$; $\Delta x=2-1=1$, $\Delta y=8-7=1$; $\Delta x=3-2=1$, $\Delta y=9-8=1$

Step2: Confirm linear function

Constant slope, each x has one y: Yes, it is a linear function.

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Problem 4

Step1: Find y-intercept ($x=0$)

$b=6$

Step2: Calculate slope $m$

$m=\frac{7-6}{1-0}=1$

Step3: Write linear equation

$y=mx+b$ → $y=x+6$

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Problem 5

Step1: Plot ordered pairs

Plot $(1,2), (2,4), (3,6), (4,8)$ on the grid (each point lies on a straight line)

Step2: Check linearity & function

Constant slope ($m=2$), each x maps to one y: Yes, it is a linear function.

Answer:

1. Domain: $\{1, 5, 6, 7\}$; Range: $\{-8, -7, 4, 5\}$; This relation is a function.
2. Ordered pairs: $(-2,-11), (-1,-9), (0,-7), (1,-5), (2,-3)$; Range: $\{-11, -9, -7, -5, -3\}$
3. Yes, the relationship is a linear function.
4. $y=x+6$
5. When plotted, the points form a straight line; this relationship is a linear function.