Representations of Functions: Determine whether the table represents a function

It is important to remember that a constant function describes a situation where, as the X value increases, the Y value remains constant.

In the table, we can see that there is a constant change in the X values, specifically an increase of 2, while the Y value remains constant.

Therefore, the table does indeed describe a constant function.

To solve this problem, we'll follow these steps:

• Step 1: Identify the given pairs of $(X, Y)$.
• Step 2: Verify that each $X$ maps to exactly one $Y$.
• Step 3: Conclude whether the table represents a function.

Now, let's work through each step:
Step 1: The pairs given are: $(-2, 1)$, $(2, 6)$, $(6, 11)$, $(10, 16)$, $(14, 21)$.

Step 2: For each input value $X$, we check its corresponding output $Y$:

• $X = -2$ maps to $Y = 1$
• $X = 2$ maps to $Y = 6$
• $X = 6$ maps to $Y = 11$
• $X = 10$ maps to $Y = 16$
• $X = 14$ maps to $Y = 21$

Step 3: Since each $X$ value has exactly one corresponding $Y$ value, the table represents a function.

Yes

To determine if the table represents a constant function, we need to examine the Y-values corresponding to the X-values given in the table.

• Step 1: Identify the given values from the table. The pairs are as follows: - For $X = -1$, $Y = 2$ - For $X = 0$, $Y = 4$ - For $X = 1$, $Y = 7$
• Step 2: Check if all Y-values are the same. Compare Y-values for each X-value:
- $Y = 2$ when $X = -1$, - $Y = 4$ when $X = 0$, - $Y = 7$ when $X = 1$.

Since the Y-values (2, 4, and 7) are not the same, the function is not constant.

Thus, the table does not represent a constant function. The correct choice is: No.

It is important to remember that a constant function describes a situation where as the X value increases, the function value (Y) remains constant.

In the table, we can observe that there is a constant change in X values, meaning an increase of 1, and a constant change in Y values, meaning an increase of 3

Therefore, according to the rule, the table describes a function.

It is important to remember that a constant function describes a situation where as the X value increases, the function value (Y) remains constant.

In the table, we can observe that there is a constant change in X values, meaning an increase of 1, and a non-constant change in Y values - sometimes increasing by 1 and sometimes by 4

Therefore, according to the rule, the table does not describe a function

To determine if the table represents a linear function, we need to check if the slope between each consecutive pair of points is constant.
Using the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, we calculate:

• Between points $(-1, 1)$ and $(2, 2)$:
  $m = \frac{2 - 1}{2 - (-1)} = \frac{1}{3}$
• Between points $(2, 2)$ and $(6, 3)$:
  $m = \frac{3 - 2}{6 - 2} = \frac{1}{4}$

Since the slopes are not equal ($\frac{1}{3} \neq \frac{1}{4}$), the function is not linear.

Thus, the table does not represent a linear function.