Final answer:
The analysis of the statements shows that some are not universally true, while others are true for specific values or ranges of x. Relevant examples and explanations demonstrate the understanding of the functions g(x) = x^2 and h(x) = -x.
Step-by-step explanation:
Let's analyze the statements in the context of the functions g(x) = x2 and h(x) = -x
- a) This statement is not true for all values of x. For example, when x=0, both g(x) and h(x) are 0, so g(x) is not greater than h(x).
- b) Similar to statement a, this is not true for all values of x. For x=0, both g(x) and h(x) equal 0, so h(x) is not always greater than g(x).
- c) For x = -1, g(x) = 1 and h(x) = 1, so this statement is true since g(x) and h(x) are equal and g(x) is not greater than h(x).
- d) The statement provided is not relevant to this question, as it pertains to vector diagrams and field vectors.
- e) For positive values of x, g(x) = x2 will always be positive, and h(x) = -x will always be negative. Therefore, for positive values of x, g(x) is indeed greater than h(x), making this statement true.
- f) For negative values of x, g(x) = x2 will still be positive, whereas h(x) will be positive as well because the negative x multiplied by the negative sign of h(x) gives a positive result. This means that g(x) might not be always greater than h(x) for negative values of x, so this statement is not generally true.