1. What are the first 3 terms of the sequence represented by the expression n(n – 2) – 4 ?
2. Given the function rule f(x) = x2 – 4x + 3, what is the output of f(–2)?
3. Suppose you earn $10 each hour you work. Write a function describes the relationship
between your total earnings E and the number of hours you work, h?
4. You charge $3.50 per hour to mow lawns plus $10 transportation fee. Write a function
for x hours and y charges.
5. You mow for 9 hours in the above equation, how much do you charge the customer for
mowing his lawn?
6. Write a function for the table in the form y=mx + b
x –3 –2 –1 0 1
y –17 –14 –11 –8 –5
7.
write a function for the graph in the form y=mx+b
Sorry, as an AI language model, I don't have the ability to display images. Please provide information about the graph or provide an image for reference.
1. To find the first 3 terms of the sequence represented by the expression n(n – 2) – 4, we substitute n = 1, 2, and 3 into the expression:
For n = 1: 1(1 – 2) – 4 = (-1) - 4 = -5
For n = 2: 2(2 – 2) – 4 = (0) - 4 = -4
For n = 3: 3(3 – 2) – 4 = (3) - 4 = -1
The first 3 terms of the sequence are -5, -4, and -1.
2. We are given the function rule f(x) = x^2 – 4x + 3 and need to find f(-2). To find the output, we substitute x = -2 into the function:
f(-2) = (-2)^2 – 4(-2) + 3
= 4 + 8 + 3
= 15
The output of f(-2) is 15.
3. The relationship between your total earnings E and the number of hours you work h can be described by the function E(h) = 10h. This means that for each hour you work, you earn $10, and your total earnings can be calculated by multiplying the number of hours by 10.
4. The function for x hours and y charges when you charge $3.50 per hour to mow lawns plus a $10 transportation fee would be y = 3.50x + 10. This function represents the total charges (y) based on the number of hours (x) you mow lawns.
5. If you mow for 9 hours using the equation y = 3.50x + 10, we substitute x = 9 into the equation to find the charges:
y = 3.50(9) + 10
= 31.50 + 10
= $41.50
So, you would charge the customer $41.50 for mowing his lawn for 9 hours.
6. The given table can be represented as a function in the form y = mx + b:
x y
-3 -17
-2 -14
-1 -11
0 -8
1 -5
To find the function, we can calculate the slope (m) and the y-intercept (b) using two points:
Using the points (-3, -17) and (0, -8):
m = (y2 - y1) / (x2 - x1) = (-8 - (-17)) / (0 - (-3)) = 9 / -3 = -3
Now substituting one of the points into the equation y = mx + b:
-17 = -3(-3) + b
-17 = 9 + b
b = -17 - 9
b = -26
The function for the table in the form y = mx + b is y = -3x - 26.
7. Unfortunately, without information about the given graph, it is not possible to determine the equation in the form y = mx + b. To write a function using this form, we need the slope (m) and the y-intercept (b), which are not provided in the question.
1. To find the first 3 terms of the sequence represented by the expression n(n - 2) - 4, we can substitute different values of n into the expression to get the corresponding terms.
- When n = 1, the expression becomes 1(1 - 2) - 4 = -5.
- When n = 2, the expression becomes 2(2 - 2) - 4 = -4.
- When n = 3, the expression becomes 3(3 - 2) - 4 = 5.
Therefore, the first 3 terms of the sequence are -5, -4, and 5.
2. The function rule f(x) = x^2 - 4x + 3 represents a quadratic function. To find the output of f(-2), we substitute -2 into the function:
f(-2) = (-2)^2 - 4(-2) + 3
= 4 + 8 + 3
= 15.
So, the output of f(-2) is 15.
3. To write a function that describes the relationship between your total earnings (E) and the number of hours you work (h), we can use the given information that you earn $10 per hour.
Therefore, the function can be written as E(h) = 10h, where E(h) represents your total earnings and h represents the number of hours you work.
4. To write a function that represents the charges for mowing lawns, which includes $3.50 per hour (x hours) and a $10 transportation fee (y charges), the function can be written as:
Charges(x) = 3.50x + 10, where Charges(x) represents the charges and x represents the number of hours.
5. If you mow for 9 hours according to the function Charges(x) = 3.50x + 10, to calculate how much you charge the customer, substitute x = 9 into the equation:
Charges(9) = 3.50(9) + 10
= 31.50 + 10
= $41.50.
Therefore, you charge the customer $41.50 for mowing his lawn for 9 hours.
6. To write a function for the given table in the form y = mx + b, we can find the slope (m) and the y-intercept (b).
To find the slope (m), choose two points from the table, let's say (-2, -14) and (1, -5).
m = (change in y) / (change in x)
m = (-5 - (-14)) / (1 - (-2))
= (-5 + 14) / (1 + 2)
= 9 / 3
= 3.
Now, let's substitute the slope (m = 3) and one of the points (x = 1, y = -5) into the slope-intercept form y = mx + b to find the y-intercept (b):
-5 = 3(1) + b
-5 = 3 + b
b = -8.
Therefore, the function for the table is y = 3x - 8.
7. Without the specific graph provided, it is not possible to write a function for the graph in the form y = mx + b. To determine the function, the coordinates of two points on the graph would be needed. Then, we could calculate the slope (m) and the y-intercept (b) to complete the equation y = mx + b.