Ask your homework questions to teachers and professors, meet other students, and be entered to win $600 or an Xbox Series X 🎉Join our Discord!

Like

Report

Numerade Educator

Like

Report

Problem 8 Easy Difficulty

Determine whether the curve is the graph of a function of x. If it is, state the domain and range of the function.

Answer

Domain: $x \in[-2,2] ;$ Range: $y \in[-1,2]$

Discussion

You must be signed in to discuss.

Video Transcript

when you're looking at a graph. If you want to determine if it's a function, you want to check to see if it passes the vertical line test. Remember, for a function. Every X value must have no more than one y value. So if you pass a vertical line through, you could only go through one point. So if I pass vertical line through lines through at various places here, notice I only go through one point. So yes, this is a function now. What's its domain and what's its range? So for the domain, we want to know what X values it goes through notice. It starts at an X value of negative two and goes over to an X value of two. So the domain in interval notation is negative. 222 That's equivalent to saying negative two is less than or equal to X is less than or equal to two. How about the range? So the range would be the Y values that it's going through. Notice that it's going through a Y value as low as negative one and as high as two and everything in between, so the range would be the interval from negative 1 to 2, and if you writing that as an inequality, it would be negative. One is less than or equal to why is less than or equal to two.

Oregon State University
Top Calculus 3 Educators
Catherine R.

Missouri State University

Caleb E.

Baylor University

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University