Question

The function f(x) is given by the set of ordered pairs. {(1,0), (–10,2), (0,6), (3,17), (–2,–1)} Which equation is true?

Answer 1

The function $f\left( x \right)$ is given by the ordered pair $\boxed{\left( {0,6} \right)}$ or $\boxed{f\left( 0 \right) = 6}.$

Further explanation:

In the interval $\left( {x,y} \right)$ the first value represents the $x$ and the second value is $y$.

The x coordinates are the domain of the function and the y coordinates are the range of the function.

Given:

The options are as follows,

(a). $f\left( { - 10} \right) = 1$

(b). $f\left( 2 \right) = - 10$

(c). $f\left( 0 \right) = 6$

(d). $f\left( 1 \right) = - 10$

Explanation:

The sets of ordered pairs are $\left( {1,0} \right), \left( { - 10,2} \right), \left( {0,6} \right), \left( {3,17} \right), \left( {-2,-1} \right)$

The x values are 1, -10, 0, 3 and -2.

The values of the function are 0, 2, 6, 17 and -1.

Option (a) is not correct.

Option (b) is not correct.

Option (c) is correct.

Option (d) is not correct.

The function $f\left( x \right)$ is given by the ordered pair $\boxed{\left( {0,6} \right)}$ or $\boxed{f\left( 0 \right) = 6}.$

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Function

Keywords: ordered pairs, (1,0), function, (-10,2), (0,6), (3,17), (-2,-1), linear function, relation table, same relation, set, set of values, set of numbers, coordinates, x-coordinate, y-coordinate.

Answer 2

The correct equation matches the set of ordered pairs of functions:

C.f (0) = 6

Further explanation

Set A to set B is said to be a function if each member of set A pairs is exactly one member of set B

So, one value of x is only assigned to one value of y

or it has only one relationship for each input value

A function can be expressed in the form of a cartesian diagram, the set of ordered pairs, or arrow diagram

If y is a function of x, then y = f (x)

where x is the independent variable and y is the dependent variable

x is the domain and y is the result area or range

A function can be write as ordered pair

Ordered pairs because we write the input first, and then the output

Can be described in form

(input, output)

or

$\large{\boxed{\bold{(x,f (x))}}$

So A function can be formed as a set of ordered pairs:

For example a set of ordered pairs

• (2,4), (3,5), (4,6)

input values ​​(as domain) 2,3,4

output values ​​(as range) 4,5,6.

We complete the questions  with answer choices :

The function f (x) is given by the set of ordered pairs. {(1,0), (–10,2), (0,6), (3,17), (–2, –1)}:Which equation is true?

f(-10)=1

f(2)=-10

f(0)=6

f(1)=-10

Let see  the answer choices :

• f (-10) = 1

values ​​x = -10, f (x) = y = 1, ordered pairs (-10,1)

• f (2) = - 10

values ​​x = 2, f (x) = y = -10, ordered pairs (2, -10)

• f (0) = 6

value x = 0, f (x) = y = 6, ordered pairs (0.6)

• f (1) = - 10

values ​​x = 1, f (x) = y = -10, ordered pairs (1, -10)

So the answer choices that correspond to the set of ordered pairs of functions above are choices C.f (0) = 6

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Keywords: domain, function, the set of ordered pairs, input, output