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.
Consider the function f(x) = x²-1.
(a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative.
Show all your steps clearly.
(b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the
graph where x 1 and x->
1+h (for a small positive value of h, illustrate conceptually). Then,
draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the
value you found in part (a).
(c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in
the context of the graph of f(x). How does the rate of change of this function vary at different
points?
1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist,
state that fact.
и
(a) f'(-5)
(b) f'(-3)
(c) f'(0)
(d) f'(5)
2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5)
=
4.
-
3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2)
and f'(2).
Does the series converge or diverge
Chapter 1 Solutions
MyLab Math with Pearson eText -- Standalone Access Card -- for Precalculus (6th Edition)
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.