Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Feb 29, 2024

Find the range of the function with domain $\{-5, -4, -2, 0, 2\}$ and codomain $\{-9, -5, -4, -3, -2, 0, 2, 5, 7\}$ .

STEP 1

Assumptions
1. The given function is represented as a set of ordered pairs.
2. The first element of each ordered pair represents the input (x-value) of the function, and the second element represents the output (y-value) of the function.
3. The range of a function is the set of all possible output values (y-values).

STEP 2

To find the range of the function, we need to list all the unique y-values from the given set of ordered pairs.

STEP 3

Extract the y-values from each ordered pair.
$\{(-2,0),(-4,-3),(2,-9),(0,5),(-5,7)\}$
The y-values are: $0, -3, -9, 5, 7$ .

STEP 4

Arrange the y-values in ascending order to make it easier to identify any duplicates and to write the range in interval notation if needed.
The ordered y-values are: $-9, -3, 0, 5, 7$ .

STEP 5

Since there are no duplicates in the y-values, we can directly write the range as the set of these y-values.
$\{y \mid y=-9,-3,0,5,7\}$

STEP 6

Compare the range we have found with the given options to identify the correct one.
The correct range of the given function is:
$\{y \mid y=-9,-3,0,5,7\}$
This matches the second option provided in the problem statement.

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