If the domain of the function y=4x+1 is 0≤x≤10, what is the function’s range?

Answer 1

Think of the domain as "the list of all x values I'm allowed to plug into the function". That's what's provided to us in this problem.

Now, think of the range as "the list of all y values that we get from plugging in the x values from the domain". So, the easiest way to do this is to plug the first and last number from the domain into the function to get the highest and lowest value in the range.

(The full, correct way to do it would be to plug all values from 0 to 10, from the domain, into the function to get the full list of values in the range. However, since this function is linear, meaning it's just multiplying a number (x) by a whole number (4) and adding 1, the lowest value from the domain will return the lowest value from the range and vice versa.)

So, for 0, you would plug it in to get 4(0)+1 = 1.

For 10, you would plug it in to get 4(10)+1 = 41

So the range would be 1<=y<=41