1.
Determine whether the figure is a graph of a function. If yes, identify the domain, range,
intercepts, and symmetry.
1.
Determine whether the figure is a graph of a function. If yes, identify the domain, range,
intercepts, and symmetry.
2.
State the domain for the following functions:
a) x 2  4 y  12  0
b) h( x) 
x4
x  16 x
c) f ( x) 
x4
x2
3
2.
State the domain in interval notation for the following functions:
a) x 2  4 y  12  0
b) h( x) 
x4
x  16 x
c) f ( x) 
x4
x2
3
3.
a) Find f ( x  1) when f ( x)  3x 2  5x  5
b) Find
f ( x  h)  f ( x )
when f ( x)  3x 2  5x  5
h
c) If f ( x)  6 x3  9 x 2  x  C and f (3)  1 , what is the value of C?
3.
a) Find f ( x  1) when f ( x)  3x 2  5x  5
b) Find
f ( x  h)  f ( x )
when f ( x)  3x 2  5x  5
h
c) If f ( x)  6 x3  9 x 2  x  C and f (3)  1 , what is the value of C?
4.
Find the values of f (2), f (1), f (4) .
For what values of x does f ( x)  1 ?
4.
Find the values of f (2), f (1), f (4) .
For what values of x does f ( x)  1 ?
5.
On what intervals is this graph increasing? Decreasing? Constant?
Where are the local minima? Local maxima?
5.
On what intervals is this graph increasing? Decreasing? Constant?
Where are the local minima? Local maxima?
6.
On the interval (-4, 5), state the coordinates of the local maxima and the local minima, if any.
Round to the nearest hundredth.
On what intervals is the function increasing? Decreasing?
f ( x)  0.3x3  0.2 x 2  4 x  5
6.
On the interval (-4, 5), state the coordinates of the local maxima and the local minima, if any.
Round to the nearest hundredth.
On what intervals is the function increasing? Decreasing?
f ( x)  0.3x3  0.2 x 2  4 x  5
7.
a) If a rock falls from a height of 90 meters on Earth, the height H (in meters) after x seconds is
approximately H ( x)  90  4.9 x 2 . When does the rock strike the ground? Round to the nearest
hundredth.
b) A projectile is fired from a cliff 500 feet above the water at an inclination of 45° to the
horizontal, with a muzzle velocity of 210 feet per second. The height h of the projectile above
32 x 2
the water is given by h( x) 
 x  500 , where x is the horizontal distance of the projectile
(210)2
from the base of the cliff. Find the maximum height of the projectile.
7.
a) If a rock falls from a height of 90 meters on Earth, the height H (in meters) after x seconds is
approximately H ( x)  90  4.9 x 2 . When does the rock strike the ground? Round to the nearest
hundredth.
b) A projectile is fired from a cliff 500 feet above the water at an inclination of 45° to the
horizontal, with a muzzle velocity of 210 feet per second. The height h of the projectile above
32 x 2
the water is given by h( x) 
 x  500 , where x is the horizontal distance of the projectile
(210)2
from the base of the cliff. Find the maximum height of the projectile.
8.
Graph the piecewise and state domain
 x 2 , x  1

a) f ( x)   x  1,  1  x  3
 2 x  2, x  3

x  2
x
1

b) f  x    x  2  2  x  3
2
4 x  3
8.
Graph the piecewise and state domain
 x 2 , x  1

a) f ( x)   x  1,  1  x  3
 2 x  2, x  3

x  2
x
1

b) f  x    x  2  2  x  3
2
4 x  3