Which of the following are true of linear functions? Select all that apply.

Question

There is exactly one output for each input.
The graph of a linear function is a straight line.
A linear function can cross the y-axis in two places.
A linear function has a constant rate of change.
A linear function must cross the x-axis.

Answer 1

The following statements about linear functions are true:

1. There is exactly one output for each input. - True. Linear functions are defined such that for every input (or x-value), there is exactly one corresponding output (or y-value).

2. The graph of a linear function is a straight line. - True. By definition, if a function is linear, its graph is a straight line.

3. A linear function can cross the y-axis in two places. - False. A linear function can only cross the y-axis at one point, which is the y-intercept.

4. A linear function has a constant rate of change. - True. By definition, linear functions have a constant slope, which means they have a constant rate of change.

5. A linear function must cross the x-axis. - False. A linear function may or may not cross the x-axis. For example, the function \(y = 2\) (a horizontal line) does not cross the x-axis.

In summary, the true statements about linear functions are the first, second, and fourth ones.