<em>The true statements are:</em>
- <em>"As x approaches negative infinity, the graph of g(x) approaches infinity. "</em>
- <em>"The </em><em>domain </em><em>of the </em><em>function </em><em>is all real numbers. "</em>
- <em>"The </em><em>range </em><em>of the </em><em>function </em><em>is all real numbers."</em>
<h3>
What statements are true?</h3>
The question is incomplete, the transformation is:
g(x) = [-(1/2)*x]^3
So we have an horizontal dilation and a reflection across the y-axis.
Now let's analyze each statement and let's see which ones are true.
a) <em>"The graph does not pass through the origin."</em>
If you evauluate g(x) in x = 0 you get:
g(0) = [-(1/2)*0]^3 = 0
So g(x) passes through the point (0, 0), meaning that this statement is false.
b) <em>"As x approaches negative infinity, the graph of g(x) approaches infinity."</em>
This is true, because the argument of the cube is a negative value.
c) <em>"As x approaches infinity, the graph of g(x) approaches infinity."</em>
This is false, when x approaches to infinity, the function tends to negative infinity.
d) <em>"The </em><em>domain </em><em>of the function is all real numbers."</em>
The function g(x) has no problematic points, so we can input any real value in it, meaning that the domain is the set of all real numbers, so this statement is true.
e) <em>"The </em><em>range </em><em>of the function is all real numbers."</em>
This is a cubic function, when x tends to infinity, the function will tend to negative infinity, wile when the x thends to negative infinity, the function will tend to infinity.
This means that the range covers the set of all real numbers, so the statement is true.
If you want to learn more about transformations, you can read:
brainly.com/question/4289712
