Are You Ready For Calculus? Name

Day 1 - Knowing your graphs!!!

1) Determine the equations of the following lines:

a) The line through (-1, 3) and (2, -4).

b) The line through (-1, 2) and perpendicular to the line 0532 yx .

2) Find the point of intersection of the lines: 073 yx and 035 yx .

3) Find the equation of the circle with center at (1, 2) that passes through the point (-2, -1).

4) Find the center and radius for the circle with the equation 2 2 6 4 3 0x y x y . (Complete the squares)

5) Find the domain of the functions:

a)

2

13)(

2

xx

xxf b)

12

35)(

x

xxg c)

6) The graph of the function )(xfy has the graph to the right:

Determine and sketch the graphs of the functions:

a) )1( xf

b) )( xf

c) )(xf

d) )( xf

7) Sketch the graphs of the functions without the use of a graphing calculator:

a) ( ) 2 4 3g x x b) 1

( ) 2 6 42

h x x

8) Simplify the difference quotient h

xfhxf )()( , where

a) 2( ) 2 3 4f x x x b) 1

1)(

xxf

9) Sketch the graph of the quadratic function without the use of a graphing calculator: 342 2 xxy

10) The graph of a quadratic function (a parabola) has x-intercepts –1 and 3 and a range consisting of all

numbers less than or equal to 4. Determine an expression for the function.

11) Find the inverse of the functions:

a) 2( ) 3 4f x x b) 15

2)(

x

xxf

12) Express x in terms of the other variables in the picture.

13) Use the pictures below to answer questions (a) and (b).

a) Find the ratio of the area inside the square but outside the circle to the area of the square in the picture (a).

b) Find a formula for the perimeter of a window of the shape in the picture (b).

14) A water tank has the shape of a cone (like an ice cream cone without ice cream). The tank is 10m high and

has a radius 3m at the top. If the water is 5m deep (in the middle) what is the surface area of the top of the

water?

15) Two cars start moving from the same point. One travels south at 100km/hr, the other west at 50 km/hr.

How far apart are they two hours later?

16) A kite is 100m above the ground. If there are 200m of string out, what is the angle between the string and

the horizontal? (Assume that the string is perfectly straight.)

17)

,1

,82

,

)(

2

x

x

xf

)5,3(

]3,2(

]2,0[

for

for

for

a) Graph the following piecewise function without the use of a calculator:

b) Evaluate f(3) = c) f(4) = d) f(0) =

(a)

r

(b)

r

r

(a)

tx

h

rx

(b)

t

h r

18) Sketch the graph of f, without the use of a calculator (sketch asymptotes/intercepts by hand)

19) , , . Evaluate the following:

a) h(g(3) = b) c)

20) Given points and , find:

a)

b) a point such that is the midpoint of

c) The value such that the point P will lie on the graph of the equation

21) Given the graph of a function , shown to the right, determine the following

a) x-intercepts

b) y-intercepts

c) How often does the line y=1 intersect the graph?

d) For what values of x is f(x) > 0 ?

e) For what values of x is f(x) increasing?