Algebra II Help: Domain & Range of f(x) = 4x + 3

[XSurferXe]

im perplexed by this question...we were never teached domain and range... so please help in an easy way with this question : "Suppose the function f(x) = 4x + 3 is defined for x > -2. "

A. Find f(-1) ... i got -1

B. Find the domain and range of F ... here I am lost PLEASE help

 

[Leong]

Domain is the the set value x for f(x) to be defined.in this case, it is given as $$x \geq\ -2$$.
Range is the set of value of f(x) for the domain. f(-2)=-5. so, the range is $$f(x)\geq \ -5$$

 

[M98Ranger]

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!