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 ) = { − 1 2 x 2 if x < 1 2 x + 1 if x ≥ 1
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 ) = { − 1 2 x 2 if x < 1 2 x + 1 if x ≥ 1
Solution Summary: The author explains the function f, which is a piecewise function.
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
)
=
{
−
1
2
x
2
if
x
<
1
2
x
+
1
if
x
≥
1
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.
2
Graph of h
6. The graph of the function h is given in the xy-plane. Which of the following statements is correct?
, the graph of h is increasing at an increasing rate.
(A) For
(B) For
(C) For
苏|4 K|4
π
π
, the graph of h is increasing at a decreasing rate.
2
0 and b>1
(B) a>0 and 01
(D) a<0 and 0
3.
Consider the sequences of functions fn: [-T, π] → R,
sin(n²x)
n(2)
n
(i) Find a function f : [-T, π] R such that fnf pointwise as
n∞. Further, show that f uniformly on [-T,π] as n→ ∞.
[20 Marks]
(ii) Does the sequence of derivatives f(x) has a pointwise limit on [-7,π]?
Justify your answer.
[10 Marks]
Good Day,
Please assist with the following.
Regards,
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.