Chris Webber

Chris Webber

9-21-09 P. 400 (94, 95)

P. 400 (94) Use a graphing utility to graph h, and use the graph to decide whether h is even, odd, or neither.

a) h(x) = cos² x

Plug function into calculator under “Y=” Y = (cos(X))²

Use X/Y chart to graph function

Analyze graph to determine whether function is even, odd, or neither

Due to graph of function being symmetric about the y-axis, function is even

P. 400 (94)

b) h(x) = sin² x

Plug function into calculator under “Y=”

Y = (sin(X))²

Use X/Y chart to graph function

Analyze graph to determine whether the function is even, odd, or neither

Due to graph of function being symmetric about the y-axis, function is even

P. 400 (95)

If f is an even function and g is an odd function, use the results of Exercise 94 to make a conjecture about h where a) h(x) = [f(x)]²

Use common understanding that when an even number is squared, it is still even. Also, refer back to number 94 to see that both functions were squared, and were even. Therefore, h(x) = [f(x)]² is an even function.

P. 400 (95) b) h(x) = [g(x)]²

Use common understanding that when an odd number is squared, it is still even. Also, refer back to number 94 to see that both functions were squared, and were even. Therefore, h(x) = [g(x)]² is an even function.