Question

How do you find the range of \[y = 3x + 4\] for the domain $ \{ - 3,0,1,4\} $ ?

Answer 1

Hint: In this question, we are given a function in terms of two variables, x and y. In the given equation y is expressed in terms of x, so x is the independent variable as it can take any value while y is the dependent variable as its value changes with the value of y. The set of values taken by x is known as the domain and the set of obtained values of y for those values of x is known as the range of the function. We are given a set of the domain and an equation, so we can easily find the range by using the above-mentioned information.

Complete step by step solution:
We are given that \[y = 3x + 4\] and we have to find its range when the domain is $ \{ - 3,0,1,4\} $ .
To find the range, we will put these values of x one by one in the given equation and get the corresponding value of y.
At \[x = - 3,\,y = 3( - 3) + 4 = - 5\]
At $ x = 0,\,y = 3(0) + 4 = 4 $
At $ x = 1,\,y = 3(1) + 4 = 7 $
At $ x = 4,\,y = 3(4) + 4 = 16 $
Hence the range of \[y = 3x + 4\] for the domain $ \{ - 3,0,1,4\} $ is $ \{ - 5,4,7,16\} $
So, the correct answer is “ $ \{ - 5,4,7,16\} $ ”.

Note: For solving this kind of question, we must know the concept of the domain and range of function clearly. Domain refers to all the possible values that x can take, that is the values of the x for which a function is defined is called the domain of the function. On putting different values from the domain, we obtain different values of the function, thus the set of all the possible values that a function can attain is called its range.