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 (c) constant. 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 constant. Then we're given a graph, we have a vertical Y axis, a horizontal X axis. They come together at the origin. The domain for what's drawn for our X axis shows from negative eight to positive eight. And it's marked off in increments of one half. And the range for what's drawn for our Y axis is from negative 50 to positive 300. And that one's marked off in increments of 10. On top of our coordinate plane, we have a function line which looks kind of like a curvy W facing upward. It begins by heading toward positive infinity for our Y values and toward negative infinity for our X values. And then it's coming down and slowly curving and it gets to the point negative 312 where it turns around and slowly begins heading upward and then it goes to the 0.0 93 at the Y axis and then starts heading down again curving slowly heading down toward the 0.3 12 at which it turns around again, heads up toward positive infinity for our Y values and positive infinity for our X values. So that's what we can see in our graph. Our answer choices are answer choice, A negative infinity to negative three and 0 to 3. Answer choice B negative 3 to 0 and three to infinity. Answer choice C negative infinity to negative three and three to infinity and answer choice D none. All right. So again, the question was where is our function constant? So what does that mean? Well, when it's talking about the function, it's talking about where the why values are constant and by constant, it means they're unchanging. So we need a stretch of our function line where the Y values don't change. What would that look like? Well, that's going to look like a horizontal line or line segment. So at any point, do we have a horizontal line or line segment with our function? And we look at this and we do not, it's always curving the why values are always changing? So there's actually no point at which our function is constant. So here the answer is no, we look at our answer choices and that matches with answer choice. D none. Well done. We'll catch you on the next one.

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

Key Concepts

Function Behavior

Intervals and Domain

Critical Points and Derivatives

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