Hi there,
I can definitely help you with this question! First, let's talk about the function f(x) = 4x + 3. This function is in the form of y = mx + b, where m is the slope and b is the y-intercept. In this case, m = 4 and b = 3.
Now, let's look at the given condition that the function is defined for x > -2. This means that the function is only valid for values of x that are greater than -2. So, any values of x that are less than or equal to -2 are not part of the domain of the function.
To find f(-1), we simply substitute -1 in place of x in the function. So, f(-1) = 4(-1) + 3 = -4 + 3 = -1. Great job, you got it right!
Now, for the domain and range of the function. The domain of a function is the set of all possible input values, or x-values, for which the function is defined. In this case, since the function is only defined for x > -2, the domain is all values of x that are greater than -2. So, in interval notation, the domain would be written as (-2, infinity).
The range of a function is the set of all possible output values, or y-values, that the function can produce. In this case, since the function is in the form of y = mx + b, we know that the range will be all real numbers because there are no restrictions on the output values. In interval notation, the range would be written as (-infinity, infinity).
I hope this helps to clarify the concept of domain and range for you. Just remember, the domain is the set of all possible x-values and the range is the set of all possible y-values. Keep up the good work!
