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 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 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 given graph represents a function, we use the vertical line test: if any vertical line intersects the graph at more than one point, the graph is not a function.

Let's apply this test to the graph:

• Examine different sections of the graph by drawing imaginary vertical lines.
• Look for intersections where more than one point exists on the vertical line.

Upon examining the graph, we observe that there are several vertical lines that intersect the graph at multiple points, particularly in areas with loops or overlapping curves. This indicates that at those $x$-values, there are multiple $y$-values corresponding to them.

Since there exist such vertical lines, according to the vertical line test, the graph does not represent a function.

Thus, the solution to this problem is that the given graph is not a function.

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.

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.