The accurate statements about the graph of g(x) are:
- As x approaches negative infinity, the graph of g(x) approaches infinity.
- As x approaches infinity, the graph of g(x) approaches infinity.
- The range of the function is all real numbers.
Let's analyze each statement about the graph of g(x) = (-1/2x):
1. The graph passes through the origin (0,0):
This statement is False. The parent function f(x) = x² passes through the origin. However, the transformation involves a reciprocal and a vertical stretch, which shifts the graph away from the origin.
2. As x approaches negative infinity, the graph of g(x) approaches infinity:
This statement is True. As x approaches negative infinity, the denominator of g(x) approaches negative infinity, making the function approach positive infinity.
3. As x approaches infinity, the graph of g(x) approaches infinity:
This statement is True. Similar to statement 2, as x approaches positive infinity, the denominator approaches negative infinity, making the function approach negative infinity.
4. The domain of the function is all real numbers:
This statement is False. The function is undefined when x = 0, as division by zero occurs. Therefore, the domain excludes 0.
5. The range of the function is all real numbers:
This statement is True. The function approaches both positive and negative infinity, covering all real numbers as the function approaches these extremes.
6. The graph of the function has three distinct zeros:
This statement is False. The function has only one zero at x = 0. However, due to the vertical stretch, the zero may not be visible on the same graph as the parent function.
Therefore, the accurate statements about the graph of g(x) are
As x approaches negative infinity, the graph of g(x) approaches infinity.
As x approaches infinity, the graph of g(x) approaches infinity.
The range of the function is all real numbers.
Complete question:
The graph of the parent function f(x) = x³ is transformed such that g(x) = (-1/2x) Which statements about the graph of g(x) are accurate? Check all that apply
The graph passes through the origin
As x approaches negative infinity, the graph of g(x) approaches infinity
As x approaches infinity, the graph of g(x) approaches infinity
The domain of the function is all real numbers
The range of the function is all real numbers.
The graph of the function has three distinct zeros