In Exercises 59-70, the domain of each piecewise function is ( − ∞ , ∞ ) a. Graph each function. b. Use your graph to determine the function's range. f ( x ) = { 0 if x < − 3 − x if − 3 ≤ x < 0 x 2 − 1 if x ≥ 0
In Exercises 59-70, the domain of each piecewise function is ( − ∞ , ∞ ) a. Graph each function. b. Use your graph to determine the function's range. f ( x ) = { 0 if x < − 3 − x if − 3 ≤ x < 0 x 2 − 1 if x ≥ 0
In Exercises 59-70, the domain of each piecewise function is
(
−
∞
,
∞
)
a.Graph each function.
b.Use your graph to determine the function's range.
f
(
x
)
=
{
0
if
x
<
−
3
−
x
if
−
3
≤
x
<
0
x
2
−
1
if
x
≥
0
Definition Definition Group of one or more functions defined at different and non-overlapping domains. The rule of a piecewise function is different for different pieces or portions of the domain.
Rylee's car is stuck in the mud. Roman and Shanice come along in a truck to help pull her out. They attach
one end of a tow strap to the front of the car and the other end to the truck's trailer hitch, and the truck
starts to pull. Meanwhile, Roman and Shanice get behind the car and push. The truck generates a
horizontal force of 377 lb on the car. Roman and Shanice are pushing at a slight upward angle and generate
a force of 119 lb on the car. These forces can be represented by vectors, as shown in the figure below. The
angle between these vectors is 20.2°. Find the resultant force (the vector sum), then give its magnitude
and its direction angle from the positive x-axis.
119 lb
20.2°
377 lb
An airplane flies due west at an airspeed of 428 mph. The wind blows in the direction of 41° south of west
at 50 mph. What is the ground speed of the airplane? What is the bearing of the airplane?
A vector with magnitude 5 points in a direction 190 degrees counterclockwise from the positive x axis.
Write the vector in component form, and show your answers accurate to 3 decimal places.
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