Question
"In order to be a linear function, a graph must.."
A be a curve.
B be a line.
D have positive slope.
E have negative slope.
F have inputs and outputs.
G pass the vertical line test.
Choose all that are correct
A be a curve.
B be a line.
D have positive slope.
E have negative slope.
F have inputs and outputs.
G pass the vertical line test.
Choose all that are correct
Answers
GPT-4o mini
To determine the characteristics of a linear function, we can analyze the options given:
A) **be a curve.** - Incorrect. A linear function must be represented by a straight line, not a curve.
B) **be a line.** - Correct. A linear function is represented by a straight line in a graph.
C) **have positive slope.** - Incorrect. While a linear function can have a positive slope, it can also have a slope of zero (horizontal line) or a negative slope, so this is not a requirement.
D) **have negative slope.** - Incorrect. Similar to option C, a linear function can have a negative slope, but it's not a requirement.
E) **have inputs and outputs.** - Correct. Linear functions (like all functions) have inputs and outputs.
F) **pass the vertical line test.** - Correct. A function must pass the vertical line test to be considered a function, which means that any vertical line drawn on the graph should intersect the line at most once.
So, the correct options are:
- **B** (be a line)
- **F** (pass the vertical line test)
- **E** (have inputs and outputs)
Thus, the answer is: **B, E, and F.**
A) **be a curve.** - Incorrect. A linear function must be represented by a straight line, not a curve.
B) **be a line.** - Correct. A linear function is represented by a straight line in a graph.
C) **have positive slope.** - Incorrect. While a linear function can have a positive slope, it can also have a slope of zero (horizontal line) or a negative slope, so this is not a requirement.
D) **have negative slope.** - Incorrect. Similar to option C, a linear function can have a negative slope, but it's not a requirement.
E) **have inputs and outputs.** - Correct. Linear functions (like all functions) have inputs and outputs.
F) **pass the vertical line test.** - Correct. A function must pass the vertical line test to be considered a function, which means that any vertical line drawn on the graph should intersect the line at most once.
So, the correct options are:
- **B** (be a line)
- **F** (pass the vertical line test)
- **E** (have inputs and outputs)
Thus, the answer is: **B, E, and F.**