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

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.

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 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.