Question

Determine which statements are true. Check all that apply.

h(x) has a constant output of –2.50.
As x increases, g(x) increases.
g(x) is greater than –2.50 for x values less than –1.
h(x) is less than –2.50 for x values greater than –2.
The input value for which g(x) = h(x) is between –1 and 0.

Answer 1

I don’t see the graph or formulas for g(x) and h(x). I can’t tell which statements are true without that. Could you either

- attach or paste the graph image, or
- give the definitions/points for g(x) and h(x) (or a table of values)?

If you want to check them yourself, here’s how to test each statement on the graph:

1. "h(x) has a constant output of –2.50."
- True if and only if h is a horizontal line at y = −2.50 (every x on the graph of h has y = −2.50).

2. "As x increases, g(x) increases."
- True if g is monotone increasing: for every pair x1 < x2, g(x1) ≤ g(x2). On the graph, g should slope upward from left to right (no overall downward trend or local decreases).

3. "g(x) is greater than –2.50 for x values less than –1."
- Check points of g for x < −1 (e.g., x = −2, −3 or the plotted left portion). If all those y-values lie above the horizontal line y = −2.50, the statement is true.

4. "h(x) is less than –2.50 for x values greater than –2."
- For x > −2, check h’s y-values: if they are all below y = −2.50, the statement is true.

5. "The input value for which g(x) = h(x) is between –1 and 0."
- Find intersections of the two graphs. If one intersection lies at an x with −1 < x < 0, this statement is true (if there are multiple intersections, you must identify the relevant one).

Send the graph or the functions and I’ll mark which statements are true.