Determine the largest open intervals of the domain over which eac...

Question

Determine the largest open intervals of the domain over which each function is (a) increasing See Example 8.

Accepted Answer

Welcome back. I am so glad you're here. We're told for the given function, find out the largest open interval of the domain over which the function is increasing. Then we are given a graph, we have a vertical Y axis, a horizontal X axis which come together at the origin. And on top of that is a graph of a function. And from negative infinity for our X values all the way to zero for our X values. The function line is at Y equals 32 and then at zero for our X values, it curves up from what looks like a parabola at that point with a vertex of 5 57 and this opens downward and then it heads curves back down toward negative infinity for our Y values and positive infinity very slowly. For our X values. For our answer choices, we have answer choice A, the interval from negative infinity to zero, answer choice B from the interval from 0 to answer choice C from the interval from five to infinity and answer choice D from the interval from 32 to 57. And none of those are inclusive. They're all with parentheses. All right. So our question was we want to know the domain over which the function is increasing. So first of all, what are we talking about with the domain? The domain is the X values? So we're looking at the X values, what about where the function is increasing? What we're saying there is where the Y values are increasing. So the function is increasing, where the Y values are increasing. So what are the XX values where the Y values are increasing? Let's look this time, we'll look at our answer choices and break it down in that way. And then we can look at it just at the graph for answer choice. A it's talking about X values from negative infinity to zero. Well, from that interval from negative infinity, all the way to zero, we have a straight line. So our Y values are not increasing. So we can eliminate answer choice A. Now for answer choice, B from 0 to 5, those X values from 0 to 5. What's happening with our Y values? They are increasing. This function is going up so that one's got possibility because it's true. Let's look at answer choice C from five to infinity. Well, from five to infinity, we can see that our function line is heading down and our Y values are therefore decreasing. So we can eliminate answer choice C and for answer choice D, what they've done here is given us from 32 to 57. Well, 32 to 57 isn't even shown on this graph and 32 to 57 those are Y values where the Y values are increasing. But that's not the domain, that's not the X values where the Y values are increasing. So we can eliminate answer choice D as well, which leaves us with answer choice B where our function is increasing in the graph. Well done. We'll catch you on the next one.

Determine the largest open intervals of the domain over which each function is (a) increasing See Example 8.

Key Concepts

Increasing Functions

Domain of a Function

Critical Points

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