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Big Ideas Math Algebra 2, 2014

BI

Big Ideas Math Algebra 2, 2014 View details

8. Analyzing Graphs of Polynomial Functions

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Exercise 45 Page 217

A function f is an even function when f(- x)=f(x) for all x in its domain. A function f is an odd function when f(- x)=- f(x) for all x in its domain.

Even

Practice makes perfect

Before we begin, let's recall two important definitions.

A function f is an even function when f(- x)=f(x) for all x in its domain.
A function f is an odd function when f(- x)=- f(x) for all x in its domain.

Let's see how the graphs of these types of functions look.

Consider the graphs above. We can see that for even functions, if (x,y) is on the graph, then (- x,y) is also on the graph. Meanwhile, for an odd function, if (x,y) is on the graph, then (- x, - y) is also on the graph. Now, consider the given function. f(x)=x^4-12x^2 Let's calculate f( - x).

f( - x)=( - x)^4-12( - x)^2

NegBaseToPosPow

(- a)^4 = a^4

f(- x)=x^4-12(- x)^2

NegBaseToPosPow

(- a)^2 = a^2

f(- x)=x^4-12x^2

Next, let's calculate - f(x).

- f(x)= - ( x^4-12x^2 )

Distribute - 1

- f(x)=- x^4+12x^2

Finally, let's think about what these results tell us.

f(x)	f(- x)	- f(x)
x^4-12x^2	x^4-12x^2	- x^4+12x^2

Since f(x)=f(- x), the function f is an even function.

Subchapter links

Communicate Your Answer p.211

Monitoring Progress p.212-215

Exercises p.216-218