solve 67 and 69 please and thank you SECTION 1.2 NATNEWATKAL woDELs: A cATLLOE o

Question

solve 67 and 69 please and thank you

SECTION 1.2 NATNEWATKAL woDELs: A cATLLOE of ESSENTIAL FUNCTIONS 25 65-70 Determine whether f is even. odd, or neither. If you have a graphing calculator, use it to check your answer visually. 67. 68, 69. Essential Functions l is a mathematical description (often by means of a function al-world phenomenon such as the size of a population, the he speed of a falling object the concentration of a product in life expectancy of a person at birth, or the cost of emission of the model is to understand the phenomenon and perhaps ut future behavior. e process of mathematical mode g. Given a real-world prob rmulate a mathematical model by identifying and naming the

Explanation / Answer

A function f(x) is even if f(-x) = f(x)

And a function f(x) is odd if f(-x) = -f(x)

67. y = x/(x+1)

let y = f(x)

=> f(x) = x/(x+1)

replace x by -x in the above equation

=> f(-x) = -x/(-x+1) = x/(x-1)

since f(-x) is neither equal to f(x) nor -f(x)

hence its neither odd or even

69. y = f(x)= 1 + 3x^2 - x^4

f(-x) = 1 + 3(-x)^2 - (-x)^4 = 1 + 3x^2 - x^4 = f(x)

hence its an even function

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