Determine whether each relation defines a function, and give the ...

Question

Determine whether each relation defines a function, and give the domain and range. See Examples 1 – 4.

Accepted Answer

Welcome back. I am so glad you're here. We're asked to identify if the given relation represents a function then determine its domain and range. We're given a graph, we have a vertical Y axis, the horizontal X axis they come together at the origin in the middle. In the second quadrant of our graph, we have a parabola and the vertex of the parabola is at negative 54. And then both of the arms of the parabola are extending toward negative infinity for the X values. Our answer choices are answer choice. A not a function domain. Open parentheses, negative infinity to negative five close bracket range, open parentheses, negative infinity to infinity. Closed parentheses. Answer trace B not a function domain, open parentheses, negative infinity to infinity, closed parentheses range open parentheses, negative infinity to negative five closed bracket. Answer choice C function domain, open parentheses, negative infinity to negative five closed bracket range, open parentheses, negative infinity to infinity, close parentheses and answer trace D function domain open parentheses, negative infinity to infinity, closed parentheses and range open parentheses, negative infinity to negative five close bracket. All right. So we recall from previous lessons that to test whether a relation represents a function, we can use the vertical line test, which means if we draw vertical lines going straight up and down, and we draw them over our function line that we're testing to see if it is a function. So our line, if we intersect the line more than once at any point, then it is not a function. But if we draw our vertical lines straight up and down over the line that we're testing to see if it is a function and anywhere we draw it, we only intersect once, then we do have a function. So let's draw some vertical lines. All right. Well, if we draw a vertical line where X equals negative eight, we see right away that we do intercept this line two times with that straight up and down line. So no, this is not a function. Now, we're asked to determine its domain and range, the domain we recall from previous lessons is all of the possible X values. So we know that it's heading toward negative infinity with these arrows on the end. So it'll keep going to negative infinity. We start negative infinity with a parentheses because we'll never quite obtain infinity. The parentheses means it's not included and we have a comma and then the farthest to the right it gets is the value of negative five. It stops and turns around at negative five. So we put negative five with a closed bracket. Because negative five is included for our line. Next, we determine the range. That's all of the possible Y values. Now, while it looks like it's mostly heading toward the left, it's very slowly heading up and very slowly heading down. So it's actually going to hit negative infinity all the way up to positive infinity as it continues for forever. So again, we open negative infinity with a parentheses. So parentheses, negative infinity comma infinity and then close again with a parentheses. And there's our domain and range. We look at our answer choices and this matches with answer choice. A well done. We'll catch you on the next one.

Determine whether each relation defines a function, and give the domain and range. See Examples 1 – 4.

Key Concepts

Function Definition

Domain and Range

Vertical Line Test

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