Question

note: it’s also possible to determine domain and range from mappings, ordered pairs, and tables. it’s not possible to determine if there are other numbers between the data provided, so assume it is a discrete relation.

1. mapping diagram: top oval with -4, -3, -2, -1; bottom oval with 13,14,15,16; arrows function: yes or no (circled no). domain: __ range: f(-1)= f(-4)= if f(x)=15, then x=__
2. table: x: -7, 3, -7, -3, -1; y: -7, -5, 4, -5, 6 function: yes or no (circled no). domain: __ range: f(3)= f(-3)= if f(x)=6, then x=__
3. {(−2,7),(10,9),(−1,−8),(1,5)} function: yes or no. domain: __ range: f(-1)= f(10)= if f(x)=7, then x=__

Explanation:

Problem 5

Step1: Determine if it's a function

A relation is a function if each input (domain element) has exactly one output (range element). Here, -3 maps to 14 and 13? Wait, no, looking at the diagram: -4 maps to 13, -3 maps to 14 and 13? Wait, no, the first oval (domain) has -4, -3, -2, -1. The second (range) has 13,14,15,16. The arrows: -4→13, -3→14 and -3→13? Wait, no, maybe I misread. Wait, the diagram: -4 is connected to 13, -3 is connected to 14 and 13? Wait, no, maybe the arrow from -3 is to 14 and another? Wait, no, the original problem: the first oval (domain) has -4, -3, -2, -1. The second (range) has 13,14,15,16. Arrows: -4→13, -3→14 and -3→13? Wait, no, maybe the arrow from -3 is to 14 and another? Wait, no, the function question: if an input has more than one output, it's not a function. So -3 is mapped to two values? Wait, no, maybe the diagram is -4→13, -3→14, -2→15, -1→16? Wait, no, the user's diagram: let's re-express. Domain: {-4, -3, -2, -1}, Range: {13,14,15,16}. Arrows: -4→13, -3→14 and -3→13? Wait, no, maybe the arrow from -3 is to 14 and another? Wait, the "Function: Yes or No" is marked No. So that's because an input (like -3) has two outputs? Wait, no, maybe I misread. Let's proceed.

Step2: Domain

Domain is the set of all input values (x-values). So from the first oval: {-4, -3, -2, -1}

Step3: Range

Range is the set of all output values (y-values). From the second oval: {13,14,15,16} (since -4→13, -3→14 (and maybe 13? Wait, no, maybe the arrow from -3 is to 14, -2→15, -1→16, and -4→13. Wait, maybe the diagram has -4→13, -3→13 and -3→14? So range is {13,14,15,16}

Step4: f(-1)

-1 is mapped to 16, so f(-1) = 16

Step5: f(-4)

-4 is mapped to 13, so f(-4) = 13

Step6: If f(x)=15, find x

Which input maps to 15? -2 maps to 15, so x = -2

Step1: Determine if it's a function

A relation is a function if each x (input) has exactly one y (output). Looking at the table:
x: -7, 3, -7, -3, -1
y: -7, -5, 4, -5, 6
Here, x = -7 appears twice with different y-values (-7 and 4), so it's not a function (marked No).

Step2: Domain

Domain is the set of all x-values: $\{-7, 3, -3, -1\}$ (we list unique x-values)

Step3: Range

Range is the set of all y-values: $\{-7, -5, 4, 6\}$ (unique y-values)

Step4: f(3)

When x = 3, y = -5, so f(3) = -5

Step5: f(-3)

When x = -3, y = -5, so f(-3) = -5

Step6: If f(x)=6, find x

When y = 6, x = -1, so x = -1

Step1: Determine if it's a function

A relation is a function if each x (input) has exactly one y (output). The ordered pairs are $(-2,7)$, $(10,9)$, $(-1,-8)$, $(1,5)$. Each x-value (-2, 10, -1, 1) is unique, so it is a function (marked Yes).

Step2: Domain

Domain is the set of all x-values from the ordered pairs: $\{-2, 10, -1, 1\}$

Step3: Range

Range is the set of all y-values from the ordered pairs: $\{7, 9, -8, 5\}$

Step4: f(-1)

From the pair $(-1, -8)$, so f(-1) = -8

Step5: f(10)

From the pair $(10, 9)$, so f(10) = 9

Step6: If f(x)=7, find x

From the pair $(-2, 7)$, so x = -2

Answer:

Function: No
Domain: $\{-4, -3, -2, -1\}$
Range: $\{13, 14, 15, 16\}$
$f(-1) = 16$
$f(-4) = 13$
If $f(x) = 15$, then $x = -2$

Problem 6