2. A portion of the graph of the function y = f(x) is shown in the figure. (a) State the domain and range of f. (b) Find the values: f(-2) and f(3). (c) Use the graph to determine each of the limits: (i) lim f(x); lim f(x); lim f(x) x--2+ x--2- x-2 (ii) lim f(x); X-3+ lim f(x); X-3¯ lim f(x). x-3 -2 ● 2+ y=f(x) Fif 2 1
2. A portion of the graph of the function y = f(x) is shown in the figure. (a) State the domain and range of f. (b) Find the values: f(-2) and f(3). (c) Use the graph to determine each of the limits: (i) lim f(x); lim f(x); lim f(x) x--2+ x--2- x-2 (ii) lim f(x); X-3+ lim f(x); X-3¯ lim f(x). x-3 -2 ● 2+ y=f(x) Fif 2 1
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 35E
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Transcribed Image Text:2. A portion of the graph of the function
y = f(x) is shown in the figure.
(a) State the domain and range of f.
(b) Find the values: f(-2) and f(3).
(c) Use the graph to determine each of
the limits:
(i) lim f(x); lim f(x); lim f(x)
x-2+
x-2-
x-2
(ii) lim f(x);
lim f(x);
x-3
lim f(x).
x+3
3. The graph of the function y = k(x) is
shown in the figure.
(a) Write a piecewise formula for the
function k.
(b) Evaluate the one-sided limits of
k at x = 1 algebraically, by using
your formula from part (a).
y=f(x)
1+
fif
1
-1-
2
1.5
1
4. Let f(x) = |x| and g(x) = x - 3.
(a) Determine the formulas for each of the related composite functions:
h(x) = (fog)(x) = f(g(x))
s(x) = (gof)(x) = g(f(x))
t(x) = (gofᵒg)(x) = g(f(g(x))).
5. (a) Find the values of x₁ and x₂ in the figure.
(b) Find the largest positive number 8 such that:
|-1|<0.1 whenever 0<|x-1|<8.
Hint:
Choose to be the minimum value of |x-1| for i = 1,2.
(b) Plot graphs of all the functions: f,h, s, and t in the same coordinate plane.
Use different colors for distinction.
y=k (x)
Z
10=1+0.1-
1
10-1-0.1-
x₁ 1
y =
T
x₂
X
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