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

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.

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 hour ago

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.