Answered

Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Is the function is even, odd or neither? How do you know?

Is The Function Is Even Odd Or Neither How Do You Know class=

Sagot :

bradley2005scopb88it

Answer:

Step-by-step explanation:

A function is even if [tex]f(x)=f(-x)[/tex], or if the graph has a rotational symmetry about the x-axis. A function is odd if [tex]f(x)=-f(-x)[/tex]. For example, if you were to reflect that graph about the y-axis. Would it present symmetry?

From the graph we know from the fundamental theorem of Algebra that since f has 3 distinct roots, and changes directions three times, we are dealing with a cubic equation in the form of [tex]f(x)=x(x+2)(x-2)[/tex]

Since the equation is known, try the formulas

First, test for an even function, [tex]f(x)=f(-x)[/tex], this means that for our function, f, [tex]f(2)=f(-2)[/tex] see if this holds true

[tex]2(2+2)(2-2) = -2(-2+2)(-2-2)\\2(4)(0)=-2(0)(-4)\\0 = 0[/tex]

This means that the function is even.

Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.