The graph of f is shown on the coordinate plane. Selected values for g are shown in the table. Graph of f 4 3 2 1 04 -1 -2 -3 -48 x-values -6 -2 -4 g(x) values Limit values of g(x) x-2° 1 -2 0 4 ▼ 0 5 3 a. Use the graph of f and the table of g to determine 4 lim X-6 6 2 lim g(x)=5 lim g(x)=4 lim g(x)=2 lim g(x) = -2 6 2f(x)²-3 f(g(x)) 8 according to limit theorems.
The graph of f is shown on the coordinate plane. Selected values for g are shown in the table. Graph of f 4 3 2 1 04 -1 -2 -3 -48 x-values -6 -2 -4 g(x) values Limit values of g(x) x-2° 1 -2 0 4 ▼ 0 5 3 a. Use the graph of f and the table of g to determine 4 lim X-6 6 2 lim g(x)=5 lim g(x)=4 lim g(x)=2 lim g(x) = -2 6 2f(x)²-3 f(g(x)) 8 according to limit theorems.
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter8: Introduction To Functions
Section8.8: Linear And Quadratic Functions
Problem 2WE
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Question
Solve it on the paper. Please use the limit rule below!!
The limit rule is lim(x->c) f(g(x)) = f( lim_(x->c) g(x)) so you take the limit as x approaches 6 of g(x) then you can take the function value of f at that number.
You need to break apart each thing. Look at the subtraction in the numerator. Then the first term in the numerator also has a constant in front so you bring the constant out front and the limit just goes with the f(x)
and then you also have a denominator so the limit can go with that as well, but that is a composition so you bring the limit inside the composition.
Transcribed Image Text:The graph of f is shown on the coordinate plane. Selected values for g are shown in the table.
Graph of f
4
3
V
2
1
0
-1
-2
-3
-4
x-values
-6
-2
g(x) values
Limit values of g(x) x-2
-4
1
lim_g(x)=5
0
4
0
5
3
2
a. Use the graph of f and the table of g to determine
4
lim
X-6
6
2
lim
im g(x)=4 lim g(x)=2 lim g(x)=-2
X→-1
X-5
X-6
6
2f(x)²-3
f(g(x))
8
according to limit theorems.
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