Question

graph the linear function f(x)=3x. identify if it is a constant function. give the domain and range.

use the graphing tool to graph the equation

is the function a constant function?

• no

x yes

what is the domain? select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the domain is a value or list of distinct values,
(type an integer or a simplified fraction. use a comma to separate answers as needed.)
b. the domain in interval notation is
(type your answer in interval notation.)

Explanation:

Step 1: Determine if it's a constant function

A constant function has the form \( f(x) = c \) where \( c \) is a constant (the output doesn't change with \( x \)). The function \( f(x) = 3x \) has a variable \( x \) multiplied by 3, so as \( x \) changes, \( f(x) \) changes. Thus, it's not a constant function.

Step 2: Find the domain of \( f(x) = 3x \)

The domain of a linear function (a polynomial of degree 1) is all real numbers because there are no restrictions on the values \( x \) can take (no division by zero, no square roots of negative numbers, etc.). In interval notation, all real numbers are represented as \( (-\infty, \infty) \).

Step 3: Find the range of \( f(x) = 3x \)

For \( f(x) = 3x \), as \( x \) takes all real values (from \( -\infty \) to \( \infty \)), multiplying by 3 will also give all real values for \( f(x) \). So the range is also all real numbers, \( (-\infty, \infty) \).

Answer:

s:

• Is the function a constant function? No
• Domain (interval notation): \( (-\infty, \infty) \)
• Range (interval notation): \( (-\infty, \infty) \)