Question

what is a linear function? a function that creates a straight line when graphed, with the form f(x) = mx + b. a function that oscillates between two values and is represented by a sine wave. a function that creates a curve when graphed, with the form f(x) = ax^2 + bx + c. a function that has no slope and is represented by a horizontal line.

Explanation:

To determine the correct definition of a linear function, we analyze each option:

• The first option: A linear function has the form \( f(x)=mx + b \) (where \( m \) is the slope and \( b \) is the y - intercept) and its graph is a straight line. This matches the definition of a linear function.
• The second option: A function that oscillates between two values and is represented by a sine wave is a trigonometric (sine) function, not a linear function.
• The third option: A function of the form \( f(x)=ax^{2}+bx + c \) is a quadratic function, whose graph is a parabola (a curve), not a straight line, so it is not a linear function.
• The fourth option: A function with no slope (a horizontal line) is a special case of a linear function with \( m = 0 \), but the first option gives the general form and the correct description of a linear function's graph (a straight line) and its equation form.

Answer:

A function that creates a straight line when graphed, with the form \( f(x)=mx + b \)