Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
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.
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.