Answer:
f(x) = 4x+5 ; 0 ≤ x ≤ 50
The range is the possible output values of f(x)
4(0) + 5 = 5 smallest output value in range
4(50) + 5 = 55 largest output value in range
The outputs are between 5 and 55 including the endpoints so
the range is [5, 55]
For a function y = f(x) we define the domain as the set of the possible inputs (the set of the values of x) and the range as the set of the possible outputs (the set of the values of y).
Here we will get the range: 5 < y < 205
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We have the function:
f(x) = 4*x + 5
And the domain is:
0 < x < 50
Note that neither 0 nor 50 are in the domain.
To get the range, we need to find the minimum and maximum of the function in the domain. Because the function is linear with a positive slope, the minimum will be for the smaller value in the domain and the maximum will be for the maximum value in the domain.
This means that the range is:
f(0) < y < f(50)
Where we use the same symbols that are used in the domain.
f(0) < y < f(50)
4*0 + 5 < y < 4*50 + 5
5 < y < 205
Finally, we can conclude that the range is 5 < y < 205. (Again, note that neither 5 nor 205 are in the range).
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