Question 1 A) Use the table to answer the question. x y 0 −10−10 1 −9−9 2 −8−8 3 −7−7Using function notation, what is the equation described in the table?(1 point) f(x)=f(x)=$$x+x+$$ Question 2 A) Use the image to answer the question. This map shows ordered pairs that belong to the function f(x)=x2f(x)=x2. What is the missing value? (1 point) $$ Question 3 A)What number would be output when an input of 4 is evaluated using the rule shown in the image? Enter your response in the output box. (1 point) $$ Question 4 A)The number of bugs doubles every 4 days. If the bug population starts with 6 bugs, then the equation A(t)=6(2)0.25tA(t)=6(2)0.25t can represent the number of bugs. Find the value for A(8)A(8).(1 point) The number of bugs after 8 days is $$. Question 5 A)The distance away from the city of Bloomsfield is a function of time. The function D(h)=440−65hD(h)=440−65h represents the distance in miles away from Bloomsfield as you travel toward the city, based on the number of hours, h , you have traveled. Find the distance left to get to Bloomsfield after 312312 hours of traveling. Enter your response in decimal form.(1 point) The distance that you have left to travel is $$ miles.

Let's go through each question one by one.

Question 1: Based on the table:

|x|y| |---|---| |0|-10| |1|-9| |2|-8| |3|-7|

The relationship between x and y appears to be linear and can be written as: \[ f(x) = -10 + x \]

So, the function notation is: \[ f(x) = -10 + x \]

Question 2: Without the image, I cannot determine the missing value in the function \( f(x) = x^2 \) directly. If you have specific ordered pairs or a specific missing point, please provide those details.

Question 3: Again, without the image, I cannot provide the output for an input of 4. Please provide the rule or formula associated with that image to proceed.

Question 4: We are given the equation \( A(t) = 6(2)^{0.25t} \). To find \( A(8) \):

1. Substitute \( t = 8 \): \[ A(8) = 6(2)^{0.25 \times 8} = 6(2)^{2} = 6 \times 4 = 24 \]

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

Question 5: We are given the function \( D(h) = 440 - 65h \) and we need to find the distance after \( h = 3123 \) hours:

1. Substitute \( h = 3123 \): \[ D(3123) = 440 - 65 \times 3123 \]

Calculating \( 65 \times 3123 = 202995 \):

Now substitute: \[ D(3123) = 440 - 202995 = -202555 \]

Since a negative distance doesn't make sense in this context, it would imply that you have already passed Bloomsfield by a considerable distance. In the context of the problem, you would say the distance left to travel is \( 0 \) miles or that you have passed the city by 202,555 miles.

Please ensure you check these calculations for any input or function errors where necessary!

Q1 and 5 are wrong

Let’s re-evaluate Questions 1 and 5.

Question 1:

Looking closely at the table again:

| x | y | |---|-----| | 0 | -10 | | 1 | -9 | | 2 | -8 | | 3 | -7 |

From this table, we can determine the equation relating \( x \) to \( y \). It appears simply that for each increase of 1 in \( x \), \( y \) increases by 1, starting from -10.

The correct function can be derived like this:

When \( x = 0 \), \( y = -10 \).

When \( x = 1 \), \( y = -9 \).

The pattern indicates: \[ y = -10 + x \] Thus, in function notation, this can be expressed as: \[ f(x) = x - 10 \]

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Question 5:

Given the function \( D(h) = 440 - 65h \), your question was to find the distance remaining after \( h = 3123 \) hours. Let's do this carefully again:

Substituting \( h = 3123 \): \[ D(3123) = 440 - 65 \times 3123 \] Calculating \( 65 \times 3123 \): \[ 65 \times 3123 = 202995 \] Then, \[ D(3123) = 440 - 202995 = -202555 \]

However, the context of this problem indicates that a negative distance indicates the distance to the city has been exceeded and does not convey logical meaning for our scenario here.

If you are interpreting it as distance left to travel, it is indeed negative, which indicates that you are far past the city of Bloomsfield. Therefore, if we're interpreting distance in terms of needing a positive output, the correct interpretation is to say that you have gone beyond the city by 202,555 miles.

If there's any additional context or rules regarding how to deal with negative outputs, please let me know!

Thank you for your patience, and I hope this clarifies the questions correctly!

Q1 equation
f(x)=___x+____

Based on the table provided:

| x | y | |---|-----| | 0 | -10 | | 1 | -9 | | 2 | -8 | | 3 | -7 |

We can see the relationship between \( x \) and \( y \) is linear. As \( x \) increases by 1, \( y \) increases by 1.

To find the formula in the form \( f(x) = mx + b \):

1. The slope (\( m \)) can be determined from how much \( y \) changes per unit change in \( x \):

   • From -10 to -9 is an increase of 1 over an increase of 1 in \( x \), so the slope \( m = 1 \).

2. The y-intercept (\( b \)) can be read directly from the table:

   • When \( x = 0 \), \( y = -10 \), thus \( b = -10 \).

So putting this together, the equation of the function is: \[ f(x) = 1x - 10 \]

In the format you specified:

• \( f(x) = __x + __ \)
• The values are: \( f(x) = 1x + (-10) \)

Thus:

• First blank (slope): 1
• Second blank (y-intercept): -10

Finally, the complete equation would be: \[ f(x) = 1x - 10 \]

Please fill in the blanks:

• \( f(x) = 1x + (-10) \) or simply \( f(x) = 1x - 10 \) based on your initial format.

Q2 graph
x y
-2 ----> 4
-1-----> 1
0------> 0
1------> 1
Response-----> 4

Based on the information you've provided, it seems we are dealing with the function \( f(x) = x^2 \). The ordered pairs you listed represent the outputs of this function for various inputs of \( x \):

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

The mentioned "Response" indicates that when \( x = -2 \), the output value (or \( y \) value) is indeed 4.

Thus, the missing value for \( f(-2) \) is:

4

If you have any additional questions or need further clarification, feel free to ask!

Q5
The distance away from the city of Bloomsfield is a function of time. The function D(h)=440−65h represents the distance in miles away from Bloomsfield as you travel toward the city, based on the number of hours, h , you have traveled. Find the distance left to get to Bloomsfield after 3 1/2 hours of traveling. Enter your response in decimal form.(1 point) The distance that you have left to travel is miles.

Let's calculate the distance left to get to Bloomsfield after \( h = 3.5 \) hours using the function provided:

\[ D(h) = 440 - 65h \]

1. Substitute \( h = 3.5 \) into the function: \[ D(3.5) = 440 - 65 \times 3.5 \]

2. First, calculate \( 65 \times 3.5 \): \[ 65 \times 3.5 = 227.5 \]

3. Now substitute this value back into the distance equation: \[ D(3.5) = 440 - 227.5 = 212.5 \]

So, the distance that you have left to travel to get to Bloomsfield after \( 3.5 \) hours is 212.5 miles.

Final Response:

The distance that you have left to travel is 212.5 miles.