It looks like you have a linear function, $y = 5x$, and you want to evaluate it or understand its behavior over the interval from $x = 0$ to $x = 2$.

Explanation

1. Function: The equation $y = 5x$ represents a straight line passing through the origin with a slope of 5. This means for every unit increase in $x$, $y$ increases by 5 units.

2. Interval: You want to analyze the function for $x$ values from 0 to 2. This means we are only looking at $x$ values between (and including) 0 and 2.

3. Calculations:

   • When $x = 0$, $y = 5(0) = 0$.
   • When $x = 1$, $y = 5(1) = 5$.
   • When $x = 2$, $y = 5(2) = 10$.

4. Graphical Interpretation: Plotting these points on a graph will give a straight line segment starting from $(0, 0)$ and ending at $(2, 10)$.

Additional Analysis

If you want to find more properties like the area under the curve from $x = 0$ to $x = 2$ or any other particular attribute, I can assist with that as well.

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Would you like more details on this function? Here are some related questions that you might find interesting:

1. What is the slope and y-intercept of the function $y = 5x$?
2. How do you calculate the area under $y = 5x$ from $x = 0$ to $x = 2$?
3. What would be the result of shifting the line $y = 5x$ by 3 units up?
4. How do we find the derivative and integral of $y = 5x$?
5. What are the values of $y$ at $x = 0.5, 1.5$, and $2.5$?

Tip: Always check the interval and domain of your function before analyzing it further. This will ensure you are focusing on the correct portion of the graph or values.