To determine which statements are true, let's break down each statement one by one and analyze it based on the behavior of the functions $g(x)$ and $h(x)$. I'll assume that you have the functions or their graph available, but since the functions are not explicitly given here, I'll explain how you can check each statement for truth:

Statement 1: $h(x)$ has a constant output of –2.50.

• If $h(x)$ is a constant function with an output of –2.50, this means that for all values of $x$, the output is always –2.50.
• True if $h(x)$ is indeed a constant function with a value of –2.50.

Statement 2: As $x$ increases, $g(x)$ increases.

• This refers to the function $g(x)$ being increasing. You would check if $g(x)$ grows larger as $x$ increases, meaning the slope is positive.
• True if $g(x)$ is an increasing function as $x$ increases.

Statement 3: $g(x)$ is greater than –2.50 for $x$ values less than –1.

• For this to be true, the graph or values of $g(x)$ must be higher than –2.50 when $x < -1$.
• True if $g(x) > -2.50$ for $x < -1$.

Statement 4: $h(x)$ is less than –2.50 for $x$ values greater than –2.

• Since $h(x)$ is said to be a constant at –2.50 (from statement 1), it cannot be less than –2.50 for any values of $x$, including $x > -2$.
• False if $h(x)$ is constant at –2.50, as it won't change and cannot be less than –2.50.

Statement 5: The input value for which $g(x) = h(x)$ is between –1 and 0.

• This implies that the two functions $g(x)$ and $h(x)$ intersect between $x = -1$ and $x = 0$. To check this, you'd need to know where their values are equal within this range.
• True if there exists an intersection of $g(x)$ and $h(x)$ in the interval $(-1, 0)$.

Summary:

• The true statements are likely:

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

• The false statement is: 4. $h(x)$ is less than –2.50 for $x$ values greater than –2.

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Would you like further explanation of any of the steps or more details?

Here are 5 related questions to consider:

1. How do you determine if a function is increasing or decreasing?
2. What are the conditions for two functions to intersect?
3. How would you graph a constant function like $h(x) = -2.50$?
4. Can a constant function ever be less than its own value at different points?
5. How would you solve $g(x) = h(x)$ algebraically if the functions were given?

Tip: When comparing functions graphically, intersections are points where the functions have the same value at the same input!