What is a reasonable range and domain for y =128x + 50

Question

And any clarification on range and domain would be appreciated

Answer 1

Domain and Range of a graph help to describe the how a graph should look.

DOMAIN or all possible x-values (inputs), will tell us how far left to right the graph will go.

RANGE or all possible y-value (outputs), will tell us how far the graph goes from bottom to top.

To find DOMAIN:

Step 1: Follow the graph of the function to its left- most point (smallest x-value on the x-axis). This number will be the left boundary. If there is an arrow, then we say that the graph goes to −∞ (negative infinity).

Step 2: Follow the graph of the function to the right -most point (largest x-value on the x- axis). If there is an arrow, then we say that the graph goes to positive infinity or just ∞.

Step 3: Follow the graph of the function to its lowest point (smallest y-value on the y-axis). This number will be the bottom- most boundary. If there is an arrow, then we say that the graph goes to −∞ (negative infinity).

Step 4: Follow the graph of the function to the highest point (largest y-value on the y- axis). If there is an arrow, then we say that the graph goes to positive infinity or just ∞.

Answer to your question: In this particular problem, the graph of y= 128x +50 is linear, we see arrows on both ends, the answer can be described in two ways

Interval Notation: Set Builder Notation

Domain: (-∞ , ∞) Domain: All real numbers

Range: (-∞ , ∞) Range: All real numbers

Answer 2

I have a little bit to add to the existing answers. The first is that it is hard to think about the domain with out a graph. Think of the domain as all the possible inputs for x that do not "break" the function. What breaks a function - dividing by zero, or taking the square root of a negative number - expressions that are undefined in the real numbers. Since y=28x +50 has no division or square roots, there are no values of x that would "break" the function. This means that all values of x are part of the domain.

There are several ways to annotate the domain or range including bracket notation (mentioned in the other responses). You could also write the domain as an inequality like this : -∞ < x < ∞ (note that we don't include equal to infinity). You can also use : x ∈ R (where R is the fat R), which just says that x is an element of the real numbers.

Answer 3

Hi J.B.!

So to define domain and range:

Domain = all of the input values that will satisfy your function (so the X values)

Range = all of the output values that are possible from your function (the Y values)

This is a linear equation that is in the form of y=mx+b...and in this case the domain will be all real numbers. (you can input any number for X from negative to positive infinity). Likewise, the range will be all real numbers as well!

You can express domain and range in different notations, but will commonly be written as an interval (-∞, ∞) when it is all real numbers.

There will be limits or boundaries to domain and range when you get different types of functions (ex: quadratic)