Which function rule represents the data in the table below?
Input (x) 1, 2, 3, 4, 5
Output(y) 9, 14, 19 ,24 ,29
a. y=4+5x
b. y=3+6x
c. y=5+4x
d. y=6+3x
help me pls
The table shows that for every increase of 1 in x, y increases by 5. We can start with y = 5x (which represents a slope of 5) and then add a constant to match the output values in the table. If we add 4 to y=5x, we get:
y = 5x + 4
Let's check if it matches the output values:
- When x = 1, y = 5(1) + 4 = 9 (matches the table)
- When x = 2, y = 5(2) + 4 = 14 (matches the table)
- When x = 3, y = 5(3) + 4 = 19 (matches the table)
- When x = 4, y = 5(4) + 4 = 24 (matches the table)
- When x = 5, y = 5(5) + 4 = 29 (matches the table)
Therefore, the function rule that represents the data in the table is:
y = 5x + 4
The answer is (c) y=5+4x.
Hey bot can you figure this out for me
Which function rule represents the data in the table
X -3 -2 -1 0 1
Y 1 -2 -5 -8 -11
The table shows that for every increase of 1 in x, y decreases by 3. We can start with y = mx + b (where m is the slope and b is the y-intercept) and then plug in one of the input-output pairs to solve for b. Let's use the first pair (-3, 1):
1 = m(-3) + b
Simplifying the equation, we get:
1 = -3m + b
Now, let's use the third pair (-1, -5) to solve for m:
-5 = m(-1) + b
Simplifying the equation, we get:
-5 = -m + b
We can solve for b in terms of m by subtracting the second equation from the first:
1 - (-5) = -3m + m + b - b
6 = -2m
m = -3
Plugging m = -3 into any of the two equations above, we get:
1 = (-3)(-3) + b
b = -8
Therefore, the function rule that represents the data in the table is:
y = -3x - 8
The answer is (d) y = -3x - 8.
hey bot got another question
which quadratic rule represents the data in the table
X -1 0 1 2 3
Y 4 5 4 1 -4
We can start by noticing that the table is not showing a perfect quadratic pattern, since the middle term is not exactly double or half of the first and last terms. However, we can still try to find an approximate quadratic rule using the method of finite differences. We will create a new table with the differences between consecutive output values:
X -1 0 1 2 3
Y 4 5 4 1 -4
Δ1 1 -1 -3 -5
Δ2 -2 -2 -2
In the second row of differences, we can see that the differences are constant at -2. This tells us that the original sequence of values can be modeled by a quadratic function. We can apply the formula for a quadratic function:
f(x) = ax^2 + bx + c
To find the coefficients, we can use the original output values to create a system of equations:
a(-1)^2 + b(-1) + c = 4
a(0)^2 + b(0) + c = 5
a(1)^2 + b(1) + c = 4
a(2)^2 + b(2) + c = 1
a(3)^2 + b(3) + c = -4
Simplifying each equation, we get:
a - b + c = 4
c = 5
a + b + c = 4
4a + 2b + c = 1
9a + 3b + c = -4
From the second equation, we know that c = 5. Substituting this into the first and third equations, we get:
a - b = -1
a + b = -1
Adding these equations, we get:
2a = -2
a = -1
Substituting this into one of the equations for a and b, we get:
-1 - b = -1
b = 0
Therefore, the quadratic rule that represents the data in the table is:
f(x) = -x^2 + 5
The answer is (c) -x^2 + 5.