Question

what is true about a linear function?
the slope is the same no matter what interval it is in.
the slope varies randomly.
the slope varies depending on the interval it is in.
the slope is the same as long as the function is in an interval greater than zero.

question 2
a student says that ( f(x) = 1 ) does not have a solution set. there is no variable ( x ) in the equation where a value for ( x ) can be placed; there are no inputs, and the only output is 1.
however, this is not correct. how can a teacher or classmate respond?
\the function ( f(x) = 1 ) means that no matter what the input is, the output will always be 1. the solution set includes all of the points on this horizontal line.\
\the function ( f(x) = 1 ) means that no matter what the input is, the output will always be 1. the solution set includes all of the points on this vertical line.\
\the function ( f(x) = 1 ) means that the input will always be 1 and the output will always be 1. the solution set consists of the point ( (3, 3) ).\
\the function ( f(x) = 1 ) means that the input will always be 1 and the output will always be 1. the solution set consists of the number 1.\

Explanation:

For Question 1:

A linear function has a constant rate of change, meaning its slope is identical across all intervals of its domain.

For Question 2:

The function $f(x)=1$ is a constant function, where every input $x$ results in an output of 1. This graphs as a horizontal line, so all points on this line make up the solution set.

Answer:

Question 1: The slope is the same no matter what interval it is in.
Question 2: "The function $f(x) = 1$ means that no matter what the input is, the output will always be 1. The solution set includes all of the points on this horizontal line."