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junior college 1 | H2 Maths
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urgent whole qn please
Date Posted: 2 years ago
Views: 471
When x = 1, f(x) takes the format 2x + 1.
f(1)
= 2 (1) + 1
= 3
Because f(x) = f(x + 4), letting x = 1,
f(5)
= f(1 + 4)
= f(1)
= 3
Clearly f is not one-to-one because some values of y can be obtained by multiple different values of x.
(In fact, in this case, every value of y is going to be met by many different combinations of x, simply because f(x) = f(x + 4) means that the function is going to be repeated over and over with a base shape which is 4 units long)
f(1)
= 2 (1) + 1
= 3
Because f(x) = f(x + 4), letting x = 1,
f(5)
= f(1 + 4)
= f(1)
= 3
Clearly f is not one-to-one because some values of y can be obtained by multiple different values of x.
(In fact, in this case, every value of y is going to be met by many different combinations of x, simply because f(x) = f(x + 4) means that the function is going to be repeated over and over with a base shape which is 4 units long)
See 1 Answer
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This is how the graph of f(x) will look like. We call this a periodic function where the graph repeats itself every four units of x, with the base shape in the region x = 0 to x = 4. The original function f(x) itself can be called a piecewise function because it is defined by two or more "pieces" or fragments of equations coming together.
You can refer to the main chat comments for part (i).
As for part (iii), the range of f simply refers to the output values (coming from the vertical axis on the graph). As we can see, the vertical values of the graph go from 1 to 5, so the range of f is given by [1, 5]. Note my usage of the open bracket "[" and the close bracket "]".
You can refer to the main chat comments for part (i).
As for part (iii), the range of f simply refers to the output values (coming from the vertical axis on the graph). As we can see, the vertical values of the graph go from 1 to 5, so the range of f is given by [1, 5]. Note my usage of the open bracket "[" and the close bracket "]".
Date Posted:
2 years ago
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