Algebraic Representation of Functions Practice Problems

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.

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 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.

To determine whether the graph represents a function, we apply the Vertical Line Test. Here are the steps we follow:

• Step 1: Visualize placing a vertical line across various parts of the graph.
• Step 2: Check if the vertical line intersects the graph at more than one point at any given position.

Step 1: On evaluating the given graph carefully, there is a notable presence of a vertical line passing through multiple y-values. Specifically, the vertical line goes from $y = -3$ to $y = 3$ at $x = 3$.

Step 2: Since this vertical line at $x = 3$ intersects the graph at an infinite number of points, it fails the Vertical Line Test.

Therefore, the graph does not represent a function. According to our analysis and the Vertical Line Test, the correct answer is No.

It is important to remember that a function is an equation that assigns to each element in domain X one and only one element in range Y

Let's note that in the graph:

$f(0)=2,f(0)=-2$

In other words, there are two values for the same number.

Therefore, the graph is not a function.