How do i find the intervals on which a function is continuous?

1 answer:

8 0

Just remember: If a function is continuous at every value in an interval, then we say that the function is continuous in that interval. And if a function is continuous in any interval, then it is a continuous function. Thus, as long as there is no break in a graph or a line the function is continuous.

You might be interested in

Over which interval does f have an average rate of change zero?

kvv77 [185]

Answer:

Step-by-step explanation:

The average rate of change is the slope. Slope has a formula that is the change in y over the change in x, which is a fraction. The only time a fraction can have a vlue of 0 is where the numerator of the fraction is equal to 0 (since we are not allowed to have a denominator of 0). If the change in y is in the top of the slope fraction, then we have to find the interval where the y values are the same. I'll show you one where the y values are not the same so you can compare it to the slope where the y values are the same. We will find the slope of choice A.

When x = -3, y = 0 so the coordinate is (-3, 0).

When x = 5, y = 5 so the coordinate is (5,4). Now let's find the slope (aka average rate of change) between those 2 coordinates:

$m=\frac{4-0}{5-(-3)}=\frac{4}{8}=\frac{1}{2}$ and the top of the fraction is a 1, not a 0, so the average rate of change between these 2 points is 1/2, not 0. Now let's do D.