176 CHAPTER 1 Functions and Their Graphs fix +h) -fx) Difference Quotient Plecew

Question

176 CHAPTER 1 Functions and Their Graphs fix +h) -fx) Difference Quotient Plecewise-Defined Functions Decreasing, or Constant Increasing: Graph of function rises from left to right. Decreasing: Graph of function falls from left to right. Constant: Graph of function does not change height from left to right. Continuous: You can draw the graph of a function without picking up the pencil. Discontinuous: Graph has holes and/or jumps. Average Rate of Change SECTION 1.2 EXERCISES . SKILLS In Exercises 1-16, determine whether the function is even, odd, or neither. 2, G(x) = 2r' + 3r' 4. g(x)=x-1+x 8. f(x)-| 12. fox) V2-x 16) h(x) 2x 14. f)v+2 911. G(t)=Vr-3 15. hx) +3 e 13, g(x) = V/r' + x In Exercises 17-28, state the (a) domain, (b) range, and (e) x-intervalís) where the function is increasing, decreasing, or constant. Find the values of (d) f(0), (e) f(-2), and (nJ(2). 18. 20.

Explanation / Answer

for even function,

f(-x) = f(x)

for odd function,

f(-x) = -f(x)

Using above definition

9.

f(x) = |x - 6|

f(-x) = |-x - 6|

there is no relation between f(x) and f(-x), so it's neither even nor odd

11.

G(t) = sqrt (t - 3)

G(-t) = sqrt (-t - 3)

there is no relation between G(t) and G(-t), so it's neither even nor odd.

13.

g(x) = sqrt (x^2 + x)

g(-x) = sqrt ((-x)^2 + (-x))

g(-x) = sqrt (x^2 - x)

there is no relation between g(x) and g(-x), so it's neither even nor odd.

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