Use the graph of the rational function to complete the following statement.

Question

As x right arrow 4 Superscript minus​, f left parenthesis x right parenthesis right arrow Modifying with underline.
-7
7
-3
3
x
y

A coordinate system has a horizontal x-axis labeled from negative 7 to 7 in increments of 1 and a vertical y-axis labeled from negative 3 to 3 in increments of 1. A graph has three branches and asymptotes x = negative 2 and x = 4. The first branch is above the x-axis and to the left of x = negative 2, approaching both. The second branch rises from left to right between the asymptotes, passing through (0, 0). The third branch is below the x-axis and to the right of x = 4, approaching both.
Question content area bottom
Part 1
As x right arrow 4 Superscript minus​, f left parenthesis x right parenthesis right arrow
  
enter your response here.

Answer 1

To determine the value of \( f(x) \) as \( x \) approaches \( 4 \) from the left (denoted as \( x \to 4^- \)), we need to analyze the behavior of the graph of the rational function in that region.

From the description, we know that the graph has a vertical asymptote at \( x = 4 \). This suggests that as \( x \) approaches \( 4 \) from the left (i.e., just smaller than \( 4 \)), the function \( f(x) \) likely tends towards either positive or negative infinity.

Since the branch of the graph that is mentioned as being between the asymptotes rises from left to right, we can infer that as we approach \( x = 4 \) from the left, \( f(x) \) will be increasing and moving towards positive infinity.

Thus, we can complete the statement:

As \( x \to 4^- \), \( f(x) \to \infty \).

However, since this is not one of the specific numerical options provided (like -7, 7, -3, or 3), and based on the behavior described, we can conclude:

As \( x \to 4^- \), \( f(x) \to +\infty \).

If you must choose from the provided options and there isn't a "tends to infinity" response available, it looks like there might be some misunderstanding or miscommunication in what was expected in the answer. Please ensure that the correct options are being provided.