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3 months ago

Which set of ordered pairs represents a function?

Mathematics

2 answers:

PIT_PIT [12.4K]3 months ago

5 0

Answer:

{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)}

Step-by-step explanation:

For the given collection to be classified as a function, each x-coordinate must correspond to just a single y-coordinate, meaning each x-value must have a distinct y-value.

In this instance, the image illustrates the graphical depiction of each set, distinguished by color.

{(2, –2), (1, 5), (–2, 2), (1, –3), (8, –1)} -> Green points

{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)} -> Blue points

{(6, 8), (5, 2), (–2, –5), (1, –3), (–2, 9)} -> Black points

{(–3, 1), (6, 3), (–3, 2), (–3, –3), (1, –1)} -> Red points

The graph reveals that the only set possessing a single y-value for each x-value is the second one (Blue points).

lawyer [12.5K]3 months ago

5 0

A function is defined as a relationship where every element from the set of first components in ordered pairs correlates to exactly one element from the set of second components.

{(2, –2), (1, 5), (–2, 2), (1, –3), (8, –1)} - this is a function

{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)} - this is also a function

{(6, 8), (5, 2), (–2, –5), (1, –3), (–2, 9)} - this represents a function

{(–3, 1), (6, 3), (–3, 2), (–3, –3), (1, –1)} - this does not qualify as a function

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3 months ago

Two functions are shown in the table below. Function 1 2 3 4 5 6 f(x) = −x2 + 4x + 12 g(x) = −x + 6 Complete the table on your o

Svet_ta [12734]

For $\fbox{\begin \\\math{x}=6\\\end{minispace}}$ the function $f(x)=-x^{2} +4x+12$ and $g(x)=-x+6$ both yield the same result.

Detailed breakdown:

The functions involved are

$f(x)=-x^{2}+4x+12$

$g(x)=-x+6$

Step 1:

Insert $x=1$ in $f(x)=-x^{2} +4x+12$ to find the value of $f(1)$ .

$f(1)=-1^{2} +4(1)+12\\f(1)=-1+4+12\\f(1)=15$

Insert $x=1$ in $g(x)=-x+6$ to find the value of $g(1)$ .

$g(1)=-1+6\\g(1)=5$

Step 2:

Insert $x=2$ in $f(x)=-x^{2} +4x+12$ to obtain the value of $f(2)$ .

$f(2)=-2^{2} +4(2)+12\\f(2)=-4+8+12\\f(2)=16$

Substitute $x=2$ into $g(x)=-x+6$ to find the value of $g(2)$ .

$g(2)=-2+6\\g(2)=4$

Step 3:

Replace $x=3$ in $f(x)=-x^{2} +4x+12$ to find the value of $f(3)$ .

$f(3)=-3^{2} +4(3)+12\\f(3)=-9+12+12\\f(3)=15$

Also, replace $x=3$ in $g(x)=-x+6$ to find the value of $g(3)$ .

$g(3)=-3+6\\g(3)=3$

Step 4:

Insert $x=4$ in $f(x)=-x^{2} +4x+12$ to find the value of $f(4)$ .

$f(4)=-4^{2} +4(4)+12\\f(4)=-16+16+12\\f(4)=12$

Also, replace $x=4$ in $g(x)=-x+6$ to obtain the value of $g(4)$ .

$g(4)=-4+6\\g(4)=2$

Step 5:

Insert $x=5$ in $f(x)=-x^{2} +4x+12$ to obtain the value of $f(5)$ .

$f(5)=-5^{2} +4(5)+12\\f(5)=-25+20+12\\f(5)=7$

Replace $x=5$ in $g(x)=-x+6$ to find the value of $g(5)$ .

$g(5)=-5+6\\g(5)=1$

Step 6:

Insert $x=6$ into $f(x)=-x^{2} +4x+12$ to find the value of $f(6)$ .

$f(6)=-6^{2} +4(6)+12\\f(6)=-36+24+12\\f(6)=0$

Also, substitute $x=6$ in $g(x)=-x+6$ to obtain the value of $g(6)$ .

$g(6)=-6+6\\g(6)=0$

Step 7:

According to the provided condition $f(x)=g(x)$ .

(a). Insert $f(x)=-x^{2} +4x+12$ and $g(x)=-x+6$ into the previously mentioned equation.

$-x^{2} +4x+12=-x+6$

(b). Multiply through by $-1$ on both sides.

$x^{2} -4x-12=x-6$

(c). Move the term $x-6$ to the left side of the equation.

$x^{2} -4x-12-x+6=0\\x^{2} -5x-6=0$

(d). Divide the middle term so that its sum equals 5 and the product equals 6.

$x^{2} -(6-1)x-6=0\\x^{2} -6x+x-6=0\\x(x-6)+1(x-6)=0\\(x+1)(x-6)=0\\x=-1,6$

From the analysis above, it is noted that for $x=6$ both functions $f(x)$ and $g(x)$ yield the same outcome.

Using a direct approach:

$f(x)=g(x)\\\Leftrightarrow-x^{2} +4x+12=-x+6\\\Leftrightarrow-x^{2} +4x+12+x-6=0\\\Leftrightarrow-x^{2} +5x+6=0\\\Leftrightarrow-x^{2} +6x-x+6=0\\\Leftrightarrow x^{2} -6x+x-6=0\\\Leftrightarrow x(x-6)+1(x-6)=0\\\Leftrightarrow(x+1)(x-6)=0\\\Leftrightarrow x=6,-1$

The table representing function $f(x)=-x^{2} +4x+12$ and $g(x)=-x+6$ is included below.

For more information:

1. What is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)? (0,–6) (0,12) (–8,0) (2,0)

2. Which is the graph of f(x) = (x – 1)(x + 4)?

6 0

2 months ago

An orchestra of 25 members bought tickets, at all different prices, to a concert, and the mean price paid was $82. A new musicia

Svet_ta [12734]

Answer:

$82.3

Step-by-step explanation:

82 multiplied by 25 equals 2050.

Adding 90 gives 2140.

Dividing 2140 by 26 results in 82.3.

5 0

3 months ago

Which of the following functions is graphed below?

Leona [12618]

We have a piecewise function consisting of a parabolic graph and a linear graph.

When the parabolic graph of $y=x^2$ is elevated by 6 units, the new equation becomes

$y=x^2+6$ .

Given that the parabola aligns with this requirement, its equation can be expressed as

$y=x^2+6$

The parabola extends to x=3, where there is an open circle at this point. Thus, we need to use a less than sign.

Next, the line's equation is determined as $y=-x+6$

Since there is a solid dot, we must employ the greater than or equal to sign.

Consequently, the piecewise function's equation is derived as

$y=\left\{\begin{matrix}
x^2=6, x$

C is the right choice.

3 0

2 months ago

Read 2 more answers