September 26, 2011
September 26, 2011
Graphing Absolute Value Compositions
Given the graph of y = f(x),
y = f(x)
reflect the portion of the graph below the
x-axis across the x-axis, leaving the
portion above the x-axis unchanged.
y = f( x ) replace the portion of the graph to the left
of the y-axis by a reflection of the portion
to the right of the y-axis across the y-axis,
leaving the portion to the right of the yaxis unchanged. (The result will show
even symmetry)
September 26, 2011
1.7 Modeling with Functions
1. A square is inscribed in a circle. Write the area
of the square as a function of the radius of the
circle.
September 26, 2011
2. An open box of maximum volume is to be made from a
square piece of material, 24 cm on a side, by cutting equal
squares from the corners and turning up the sides.
a. Write the volume, V, as a function of x.
b. Find the domain of the function.
c. Find the dimensions of the cut-out squares that will
produce a box of maximum value.
September 26, 2011
3. A small satellite dish is packaged with a cardboard
cylinder for protection. The parabolic dish is 24in. in
diameter and 6in deep, and the diameter of the cardboard
cylinder is 12in. How tall must the cylinder be to fit in
the middle of the dish and be flush with the top of the
dish?
September 26, 2011
4. A tire of a moving bicycle has radius 16in. If
the tire is making 2 rotations per second, find the
bicycle's speed in miles per hour.