For the following questions use the functions: f(x) = 4x + 2 g(x) = 2x - 3 Evaluate f(g(x)) Describe the transformation of f(x) = (4x + 2) - 1 Describe the transformation of f(x) = 4(x + 3) + 2 Describe the transformation of g(x) = 2(2x - 3) Describe the transformation of f(x) = 4(3x) + 2
Erin Larsen
Open question
2022-08-18
f(x) = 4x + 2
g(x) = 2x - 3
Evaluate f(g(x))
Describe the transformation of f(x) = (4x + 2) - 1
Describe the transformation of f(x) = 4(x + 3) + 2
Describe the transformation of g(x) = 2(2x - 3)
Describe the transformation of f(x) = 4(3x) + 2
Answer & Explanation
Heidy Phelps
Beginner2022-08-19Added 4 answers
We know that,
f(x)=4x+2 and g(x)=2x-3
(1) The value of f(g(x)) can be evaluated as
f(g(x))=4(g(x))+2
=4(2x-3)+2
=8x-12+2
=8x-10
=2(4x-5)
(2) We know that, given a function f(x), a new function f'(x)=f(x)+k, where k is a constant, is a vertical shift of the function f(x). If k is positive, the graph will shift up. If k is negative, the graph will shift down.
Hence, the transformation of f(x)=(4x+2)-1 is 1 unit down from the graph of f(x).
(3) We know that, given a function f(x), a new function f'(x)=f(x)+k, where k is a constant, is a vertical shift of the function f(x). If k is positive, the graph will shift up. If k is negative, the graph will shift down.
Hence, the transformation of f(x)=4(x + 3)+2 is 2 unit up from the graph of f(x).
Step 2(4) Given a function f(x)a new function g(x)=af(x),where a is a constant, is a vertical stretch or vertical compression of the function f(x) takes place as
1.If a>1, then the graph will be stretched.
2.If 0
Hence, the transformation of g(x) = 2(2x - 3) is that the graph of g(x)=(2x-3) will be stretched.
(5) We have,
f(x)=4(3x)+2
=12x+2
=3(4x+2-2)+2
=3(4x+2)-6+2
=3(4x+2)-4
Hence, the transformation of f(x)=4(3x)+2 is that firstly the graph of f(x)=(4x-2) will be stretched vertically by a factor 3 as and then shift 4 unit down.
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