Which of the following equations correctly describes the function in the table using function notation? x y 0 -2 2 4 4 10 6 16 (1 point) Responses f(x)=2xf of x is equal to 2 x f(x)=2x+4f of x is equal to 2 x plus 4 f(x)=3x−2f of x is equal to 3 x minus 2 f(x)=x−2

Answer 1

To determine which equation correctly describes the function represented in the table, we can analyze the provided \(x\) and \(y\) values:

\[ \begin{align*} x & : 0, 2, 4, 6 \ y & : -2, 4, 10, 16 \ \end{align*} \]

Let's evaluate the changes in \(y\) based on the changes in \(x\):

1. When \(x = 0\), \(y = -2\)
2. When \(x = 2\), \(y = 4\)
3. When \(x = 4\), \(y = 10\)
4. When \(x = 6\), \(y = 16\)

Now, let's find the differences between \(y\) values as \(x\) increases:

• From \(0\) to \(2\): \(4 - (-2) = 6\)
• From \(2\) to \(4\): \(10 - 4 = 6\)
• From \(4\) to \(6\): \(16 - 10 = 6\)

The difference in \(y\) is consistently \(6\) as \(x\) increases by \(2\).

Based on this, the relationship appears to be linear. To express the linear function in slope-intercept form \(y = mx + b\):

• The slope \(m\) can be calculated from the differences:

  \(m = \frac{\Delta y}{\Delta x} = \frac{6}{2} = 3\)

• Now, we can determine the y-intercept by substituting one of the points into \(y = 3x + b\). Let's use the point (0, -2):

  \(-2 = 3(0) + b \rightarrow b = -2\)

Thus, the linear function can be formulated as:

\[ f(x) = 3x - 2 \]

Therefore, the correct response is:

f(x) = 3x - 2

Answer 2

The function C(n)=12n+5C(n)=12n+5 gives the cost to order a necklace n, including a flat rate shipping charge.(2 points) What does C(3)C(3) represent in the context of this scenario? Which of the following inputs does not make sense in the context of this scenario?

Answer 3

The function \( C(n) = 12n + 5 \) represents the total cost of ordering \( n \) necklaces, where:

• \( 12n \) reflects the cost of the necklaces themselves (assuming each necklace costs $12),
• \( 5 \) is a flat rate shipping charge that is added regardless of how many necklaces are ordered.

Interpretation of \( C(3) \)

The expression \( C(3) \) calculates the total cost of ordering \( 3 \) necklaces. By substituting \( n = 3 \) into the function:

\[ C(3) = 12(3) + 5 = 36 + 5 = 41 \]

So, \( C(3) \) represents the total cost of ordering 3 necklaces, which amounts to $41.

Input that Does Not Make Sense

In the context of this scenario, we consider the following about the variable \( n \):

• \( n \) represents the number of necklaces ordered, which must be a non-negative integer (i.e., \( n \geq 0 \)).

Based on this understanding, the only inputs that do not make sense in this context would be:

• Negative integers (e.g., \( n = -1 \))
• Non-integer values (e.g., \( n = 2.5 \))
• Non-numeric values (e.g., \( n = "three" \))

These inputs lack a logical interpretation because you cannot order a negative quantity or a fractional or non-numeric amount of necklaces.

If you provide a specific list of inputs to evaluate against, I can indicate the particular input that does not make sense.