Review for Curve Sketching

Solving Trig

100

cos(0)=

1

200

Solve for x.  [0,2pi)

3 sin(x)=0

0 and pi

300

Solve for x [0, 2pi)

-5=-4 + tan(x)

3pi/4  and 7pi/4

400

solve for x [0, 2pi)

sec(4x)=1

x= 0, pi/2, pi, 3pi/2

500

solve for x [0, 2pi)

cot²(x)+2cot(x)-1=-2

x= 3pi/4, 7pi/4

Graphing Rational

100

What is the vertical asymptote?

y = (2x-3)
       (x-4)

x=4

200

What is the Horizontal Asymptote?

y = 2x-3
       x-4

y=2

300

Where is the hole?

y = x²-64        
       x²+9x+8

(-8, 16/7)

400

What are the x and y -intercepts?

y = a-4
      2a-8

(0, 1/2) 

*x=4 is  a HOLE not an intercept*

500

Graph the function

y =   x+4  
     4x²-4x-8

VA: x =2 and x=-1

x-intercept (-4, 0)

y-intercept (0, -1/2)

HA y=0

Holes: None

Graphing Polynomials

100

What is the degree?

f(x)=12x³-15x²+1

3

200

What is the degree?

f(x)=(x-2)(x²+7)

3

300

What is the end behavior?

y=3x⁷-15x²+11

As x approaches infinity, y approaches infinity

As x approaches negative infinity, y approaches negative infinity

400

What is the y-intercept?

g(x)=(3x-2)(x+7)(x-5)

(0,70)

500

Is x=13 a relative min or max?

y=13x(x-4)²(x-10)³(x-13)²

Relative minimum

Domain and Range

100

What is the domain?

f(x)=3x²-5

(-inf, inf)

200

What is the domain?

y= (x-5)(x+2)
     (x-2)(x+3)

(- inf, -3)u(-3, 2)U(2, inf)

300

What is the domain?

y=(x+2)(x-4)
     x²-6x+8

(-inf, 2) U (2, 4) U (4, inf)

400

What is the domain?

y=(x-2)^1/2

[2, inf)

500

What is the domain?

y=log(x+1)-2

(-1, inf)

Limits

100

What is the limit as x approaches inifnity?

y = 2x²-7x+4
       4x⁴-5x+2

1/2 (same as HA)

200

What is the limit as x approaches infinity?

y = 4x²-7x+1
        2x-1

DNE -> positive infinity (SA)

300

What is the limit as x approaches infinity?

y = x²+x
      3-x

DNE ->Negative Infinity (SA)

400

What is the limit as x approaches Negative Infinity?

y = 3x³-5x+1

Negative infinity (end behavior)

500

What is the limit as x approaches negative infinity?

y = 3x-2
      5x+1

3/5 (HA)