Math 65, Section 3.4 Square Root Functions:
I. Review:
A. Give an example of each
1. Linear function:
2. Quadratic function:
B. Domain and Range:
1. Domain
2. Range
C. Exponent Rules:
1. 0 exponent
2. Negative exponent
D. Square Roots:
1. Ball­park Approximate:
2. Simplify ­ exact
3. Calculator ­ approximate
also try 50^(1/2)
II. Graphing a square root function:
A. By hand: D:
R:
1
B. On the Calculator
C. Horizontal and Vertical Shifts:
Ex. 1: Graph by hand: x
y
D:
R:
Ex. 2: Graph by hand: x
g(x)
D:
R:
2
D. On the Calculator: describe the translations (shifts, stretches, reflections, etc.) and give the Domain and Range for each.
III. Applications of Square Root Functions:
Ex. 3: The side of a square is related to the area.
When the area is known, we can estimate the length of the side.
a) Estimate the length of the side of a square with area of b) Estimate the length of the side of a square with area of 3
Ex. 4. Velocity of a Nissan pickup is related to its stopping distance by the equation: where d is the stopping distance in feet and
v is the velocity in miles per hour.
a) How fast was he going if it took him 85 feet to stop?
b) Sketch a graph. Use the window: c) From the graph, estimate the distance required to stop when traveling at 65 mph
Ex. 5: The time, t, in seconds that it takes a pendulum to swing back and forth one, is given by:
Where l is the length of the pendulum in feet.
a) Find the time a 128­foot pendulum takes to make one back and forth swing.
b) Sketch a graph. Use the window:
c) From the graph, estimate the length of a pendulum which takes about 10 seconds to make a back and forth swing.
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