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Use the table to answer the question.

x y
0 −10

1 −9

2 −8

3 −7

Using function notation, what is the equation described in the table?(1 point)
f(x)=
x+
///???

11 answers

To find the equation described in the table, we can analyze the pairs of \( (x, y) \) values given. We can observe the change in \( y \) as \( x \) increases:

  • When \( x = 0 \), \( y = -10 \)
  • When \( x = 1 \), \( y = -9 \)
  • When \( x = 2 \), \( y = -8 \)
  • When \( x = 3 \), \( y = -7 \)

From this, we can see that for every increase of 1 in \( x \), \( y \) increases by 1. Therefore, the relationship between \( x \) and \( y \) is linear.

We can express this in function notation as:

\[ f(x) = x - 10 \]

Thus, combining these observations, the equation described in the table is:

\[ f(x) = x - 10 \]

there is two

My apologies for the oversight. Let's analyze the table again:

  • When \( x = 0 \), \( y = -10 \)
  • When \( x = 1 \), \( y = -9 \)
  • When \( x = 2 \), \( y = -8 \)
  • When \( x = 3 \), \( y = -7 \)

From the observations, it appears that \( y \) is increasing by 1 for each increase of 1 in \( x \), indicating a linear relationship.

Given the two parts of the equation you mentioned ("there is two"), let’s write the function in slope-intercept form (i.e., \( y = mx + b \)):

  1. The slope \( m \) is 1 (since \( y \) increases by 1 as \( x \) increases by 1).
  2. The initial value (when \( x = 0 \)) is \( y = -10 \), which gives us the y-intercept \( b = -10 \).

So, we can express the function as:

\[ f(x) = 1x - 10 \]

or simply:

\[ f(x) = x - 10 \]

This seems to be a single function since there's typically one equation to describe a relation between \( x \) and \( y \) unless we introduce additional constraints or conditions.

If there’s a specific second equation or aspect you're referring to, could you please clarify? This will help me assist you better!

Use the image to answer the question.

Two side-by-side shaded ovals labeled x and y each display a list of values. Five arrows point from the values in the left oval, x, to the values in the right oval, y.

This map shows ordered pairs that belong to the function f(x)=x2
. What is the missing value?

(1 point)
Remaining Attempts : 3

To find the missing value in the context of the function \( f(x) = x^2 \), we need to determine the corresponding \( y \) value for given \( x \) values from the left oval.

Since \( f(x) = x^2 \), this means that for each \( x \), we square the value to find \( y \).

Here are a few examples of how the function operates:

  • If \( x = -2 \), then \( f(-2) = (-2)^2 = 4 \)
  • If \( x = -1 \), then \( f(-1) = (-1)^2 = 1 \)
  • If \( x = 0 \), then \( f(0) = 0^2 = 0 \)
  • If \( x = 1 \), then \( f(1) = 1^2 = 1 \)
  • If \( x = 2 \), then \( f(2) = 2^2 = 4 \)

If you provide the specific values listed in the ovals or the missing value context in your question, I can help you identify the missing output value more accurately.

so bot what is the answer

To find the missing value from the function \( f(x) = x^2 \), we need to look at the values that are present in the left oval (which contains \( x \) values) and then calculate their corresponding \( y \) values (which belong in the right oval).

Here’s how the function works:

  • For each \( x \), calculate \( y = f(x) = x^2 \).

If you provide the specific \( x \) values listed in the left oval, I can compute the corresponding \( y \) values and identify the missing value for you.

Without the specific values, I can’t determine the exact missing value. Please provide those values, and I'll be glad to assist!

what is the missing value

I'm sorry for the confusion earlier. To help you find the missing value in the function \( f(x) = x^2 \), I need to know the values of \( x \) that are present and which \( y \) values are associated with them.

If you remember the specific \( x \) values listed in the left oval (the input values) and any results or pairs that were provided in the right oval (the output values), please share those so I can calculate the missing value accurately.

Example

If, for example, the values in the left oval (x values) were:

  • -2
  • -1
  • 0
  • 1
  • 2

Then the corresponding \( y \) values would be:

  • \( f(-2) = 4 \)
  • \( f(-1) = 1 \)
  • \( f(0) = 0 \)
  • \( f(1) = 1 \)
  • \( f(2) = 4 \)

If you have the pairs or some specific values you need help with, let me know!

The number of bugs doubles every 4 days. If the bug population starts with 6 bugs, then the equation A(t)=6(2)0.25t
can represent the number of bugs. Find the value for A(8)
.(1 point)
The number of bugs after 8 days is
.

To find the value for \( A(8) \) using the equation \( A(t) = 6(2)^{0.25t} \), we can substitute \( t = 8 \) into the equation.

Here’s how you calculate it:

\[ A(8) = 6(2)^{0.25 \times 8} \]

First, calculate \( 0.25 \times 8 \):

\[ 0.25 \times 8 = 2 \]

Now substitute that back into the equation:

\[ A(8) = 6(2)^{2} \]

Next, calculate \( (2)^{2} \):

\[ (2)^{2} = 4 \]

Now substitute that into the equation:

\[ A(8) = 6 \times 4 = 24 \]

Thus, the number of bugs after 8 days is 24.