Answer the questions individually and compare the results.
The distance from f(0) to f(2) is equal to 2, while all the other answers are equal to - 1.
Practice makes perfect
Let's start by looking at the graph we are given.
We can see two points on the graph, (2,0) and (0,2). Therefore, f(0)=2 and f(2)=0.
What is the average rate of change over 0≤ x≤ 2?
Let's examine the first question — what is the average rate of change over 0≤ x≤ 2? In order to find the average rate of change over the given interval we use the following formula.
Average rate of change=f(x_2)-f(x_1)/x_2-x_1
Let's substitute the given points.
The average rate of change over the given interval is equal to - 1.
What is the distance from f(0) to f(2)?
Now let's look at the next part, asking for the distance from f(0) to f(2). Since f(0) and f(2) are numbers, the distance between them is an absolute value of their difference.
The distance from f(0) to f(2) equals 2, which is not equal to - 1. We have gotten a different result from the previous section, so one of these is probably the different question we are looking for.
What is the slope of the line segment?
The next question asks for the slope of the line segment. In order to find the slope of the segment we can use the Slope Formula.
