91. Find the domain of: y=-3x+1
a. all negative numbers
b. x>0
c. all real numbers
d. x=3
Can someone please show the work and how to solve this problem. There are many of these in my lessons and I don't understand how to solve them. Do you solve for x?
The domain is all values of x for which the equation "makes sense" and can be used to calculate y. In this case, the answer is c (all real numbers).
No. You just inspect the function (in this case (-3x+1) and see if there are any values of x that would violate the fundamental laws of math. For instance, if you had (-3x+1)/(x+3) then the domain would be all values of x EXCEPT x=-3, as division by zero is NOT allowed. In your case, the domain of x is (best answer: all real numbers). X can assume any value (real or imaginary), but I suppose you are not into complex numbers yet. Let me let you jump ahead and look at that(I am so kind and generous).
What if f(x)=x/(x^2+1) Well, division by zero is not allowed, so x= sqrt(-1) is not allowed, but that is an imaginary number. So the domain for x here is all values, real and imaginary, except x=i (i=sqrt(-1))
In your problem above, all real x are allowed.
Here is a good explanation: http://www.analyzemath.com/DomainRange/DomainRange.html
To find the domain of the equation y = -3x + 1, we need to determine the range of values that x can take while still producing a valid output for y.
In this case, there are no restrictions or limitations on the values of x that could be plugged into the equation. So, the correct choice for the domain of this equation is option c: all real numbers.
To further understand why this is the case, let's break it down step by step:
Step 1: Start with the equation y = -3x + 1.
Step 2: Recall that the domain refers to the set of all possible values for the independent variable, which in this case is x. So, we need to find the range of values that x can take.
Step 3: The equation y = -3x + 1 is a linear equation, which means it represents a straight line. In a linear equation, there are no restrictions on the values of x that can be used. You can pick any real number for x, and the equation will have a corresponding y-value.
Step 4: Therefore, the domain of this equation is all real numbers. This means that x can be any number, whether positive, negative, or zero.
In conclusion, the correct answer is option c: all real numbers.
Remember, when finding the domain of an equation, you are determining the set of all possible x-values that make the equation valid.