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 have a coordinate plane, 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 is from negative 60 to positive 30. And the range for what's drawn for our Y axis is from negative 40 to positive 60. And both axes are marked off in increments of five. Then we have a function line on our coordinate plane and there's three sections to the function line. The first section from the X values of negative 60 to the X value of zero. What's drawn but really it goes from negative infinity for the X values all the way to zero, our Y values remain constant at 32. And then at the 0.0 32 we have a new section. So from the X values of zero and then all the way up to the X value of five, our Y values are increasing, they're going up. The first Y value is at 32 and it goes all the way up to 57. Then the last section from the X value of five and then it looks like it goes only to the X value of 15. But actually, it's going all the way to positive infinity. Our Y values, it starts off at 557. So that Y value starts off at 57 and then it's going all the way down at the 0.15 for the X value, it's at negative 40 for the Y value. But presumably it just keeps going toward negative infinity for our Y values as it heads toward positive infinity for our X values. So that's what's drawn for our graph. Our answer choices are answer choice, a negative infinity to zero. Answer choice B 0 to 5, answer choice C five to infinity and answer choice D 32 to 57. All right. So what are we being asked? We are asked to say where the function is constant. So what does that mean? Well, where the function is constant is where the, why values are constant? And we've already talked about that a little bit where the Y values are constant where they don't change is that first section where there's a straight line. So it's shown from negative 60 to 0 for our X values. But really, it's all the way from negative infinity to zero for our X values. And what, how are we asked to express this, we are asked to express the domain, as we said before, the domain is our X values. And that's what I've written here. The domain for each of our sections, the domain for where the Y values are constant or where the function is constant is from negative infinity to zero. Those are the X values where our Y values are constant. So that's the domain over which the function is constant. We look at our answer choices and this matches with answer choice. A 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 Domain

Constant Function

Open Intervals

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