To make sure its correct before I turn it in
Q.If f(x) is a linear function, which statement must be true?
A.f(x) has no x2-term.
Q2.The graph of a function must be linear if it has what characteristic?
A2.It has a constant slope.
Q3.If f(x) is a linear function, what is the value of n?
HERE IS THE GRAPH
I made it the best I can
[3] [7]
[7] [n]
[9] [16]
[16] [26.5]
A3.N is 11
To verify the correctness of the answer, let's analyze each question and check the given information.
Q1. If f(x) is a linear function, which statement must be true?
The statement "f(x) has no x^2-term" is a characteristic of linear functions. Linear functions are defined by having a degree of 1, which means the highest power of x is 1. Therefore, the statement is correct.
Q2. The graph of a function must be linear if it has what characteristic?
The characteristic that indicates a linear function is having a constant slope. In other words, for every unit of change in the x-axis, there is a constant corresponding change in the y-axis. So, if a function has a constant slope, it can be concluded that the graph represents a linear function. Hence, the statement is correct.
Q3. If f(x) is a linear function, what is the value of n?
To find the value of n, we can observe the given graph. The graph represents the values of f(x) for different x values. Looking at the y-values in the second column, we can notice a pattern. The difference between each pair of consecutive numbers in the y-values is constant.
From top to bottom, the differences are:
7 - 3 = 4
n - 7 = n - 7 (constant)
16 - 9 = 7
26.5 - 16 = 10.5
Since the differences are consistent, we can conclude that the slope between each pair of consecutive points is constant. In this case, the slope is given by the formula (change in y) / (change in x).
Using the first pair of points (3, 7) and (7, n), we can calculate the slope:
Slope = (n - 7) / (7 - 3) = (n - 7) / 4
Using the second pair of points (7, n) and (9, 16), we can calculate the slope:
Slope = (16 - n) / (9 - 7) = (16 - n) / 2
Setting both expressions for the slope equal to each other, we get:
(n - 7) / 4 = (16 - n) / 2
Simplifying and solving for n:
2(n - 7) = 4(16 - n)
2n - 14 = 64 - 4n
6n = 78
n = 13
Thus, the value of n is 13, not 11 as stated in your response.
Therefore, the correct answer for question 3 would be:
A3. The value of n is 13.
Q1. If f(x) is a linear function, which statement must be true?
A. f(x) has no x^2 term.
Q2. The graph of a function must be linear if it has what characteristic?
A. It has a constant slope.
Q3. If f(x) is a linear function, what is the value of n?
Here is the graph:
[3] [7]
[7] [n]
[9] [16]
[16] [26.5]
A3. To determine the value of n, we need to determine the pattern or relationship between the given values. Looking at the graph, we can see that the second column increases by a constant value each time.
To find this constant difference, we subtract the second value from the first value in each row:
7 - 3 = 4
n - 7 = n - 7
16 - 9 = 7
26.5 - 16 = 10.5
Since the difference between the second values is not constant, we can conclude that this table of values does not represent a linear function. Therefore, we cannot determine the value of n based on this given graph.
Please note that if the given graph represented a linear function, we could find the value of n by observing any of the equations that describe the linear relationship in the graph, and then substituting the corresponding x-value into the equation.
yes but we write it x^2 for x squared
yes, constant slope is linear
slope = change in y / change in x
for example
m = (16-7)/(9-3) = 9/6 = 3/2
y = (3/2) x + b
if x = 3, y = 7
so
7 = (3/2)(3) + b
14/2 = 9/2 + b
b = 5/2
so in the end
y = (3/2) x + 5/2
if x = 7
y = (3/2)(7) + 5/2
y = 26/2
y = 13
=================
check a point to be sure
if x =9
y = (3/2)9 + 5/2
y = 27/2 + 5/2 = 32/2 = 16
so my equation is right