Section 1.2 Analyzing Graphs

x is the distance from the y-axis f(x) is the distance from the x-axis p. 79 Figure 1.6 (open dot means the graph does not include

that point, closed dot means it does include the point and no dot indicates the graph continues past the view shown)

• find the domain of f• find f(-1), f(2)• find the range of f

Vertical Line Test for functions p.80

Zeros of a function the x values for which f(x) = 0 the x-intercepts set the function equal to zero and solve

for x find the zeros of the function

• f(x)=3x2+x-10• g(x)=

• h(t)= 2t-3 t+5

210 x

Increasing and decreasing functions A function is increasing on an interval if

for x1 < x2, f(x1) < f(x2)

A function is decreasing on an interval if for x1 < x2, f(x1) > f(x2)

A function is constant on an interval if for x1 < x2, f(x1) = f(x2)

p 82 ex.4

Linear Functions

f(x) = mx+b f(x) = -4x+10 Write the linear function f for which

f(1)=3 and f(4)=0

Step Functions The graph looks like stair steps One example of a step function is the

Greatest Integer Function [[x]] = the greatest integer less than or

equal to x• [[2]]• [[3.4]]• [[-4]]• [[-5.6]]• graph on p. 85

Piecewise Functions

f(x)=

2 3, 1

4, 1

x x

x x

, 0

( ) 0,0 1

1, 1

x x

f x x

x x

Even and Odd Functions (rule #12)

A function is even if for each x in the domain of f, f(-x) = f(x) (where have we seen this before?)

A function is odd if for each x in the domain of f, f(-x) = -f(x)

Are these functions even, odd, or neither?

• g(x)=x3-x• h(x)=x2+1