In Exercises 31-32, the domain of each piecewise function is (-∞, ∞). a. Graph each function. b. Use the graph to determine the function’s range. f ( x ) = { 2 x − x if x < 0 if x ≥ 0
In Exercises 31-32, the domain of each piecewise function is (-∞, ∞). a. Graph each function. b. Use the graph to determine the function’s range. f ( x ) = { 2 x − x if x < 0 if x ≥ 0
Solution Summary: The author explains how to determine the graph of the function f(x).
In Exercises 31-32, the domain of each piecewise function is (-∞, ∞).
a.Graph each function.
b.Use the graph to determine the function’s range.
f
(
x
)
=
{
2
x
−
x
if
x
<
0
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.
Match the equation, graph, and description of transformation.
Horizontal translation 1
unit right; vertical
translation 1 unit up;
vertical shrink of 1/2;
reflection across the x
axis
Horizontal translation 1
unit left; vertical
translation 1 unit
down; vertical stretch
of 2
Horizontal translation
2 units right; reflection
across the x-axis
Vertical translation 1
unit up; vertical stretch
of 2; reflection across
the x-axis
Reflection across the x
- axis; vertical
translation 2 units
down
Horizontal translation
2 units left
Horizontal translation
2 units right
Vertical translation 1
unit down; vertical
shrink of 1/2; reflection
across the x-axis
Vertical translation 2
units down
Horizontal translation 1
unit left; vertical
translation 2 units up;
vertical stretch of 2;
reflection across the x
- axis
f(x) = -
=-½ ½ (x − 1)²+1
f(x) = x²-2
f(x) = -2(x+1)²+2
f(x)=2(x+1)²-1
f(x)=-(x-2)²
f(x)=(x-2)²
f(x) =
f(x) = -2x²+1
f(x) = -x²-2
f(x) = (x+2)²
What is the vertex, increasing interval, decreasing interval, domain, range, root/solution/zero, and the end behavior?
The augmented matrix of a linear system has been reduced by row operations to the
form shown. Continue the appropriate row operations and describe the solution set of the
original system.
1 -1
0 1 -2
00-4
0-6
0
0
1
- 3
3
0
001
4
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