3.2 Zeros of Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does the term 'zero of a function' mean?

Back

The zero of a function is the value of x for which the function f(x) equals zero. It is the x-coordinate where the graph of the function intersects the x-axis.

Front

How do you find the zeros of a linear function?

Back

To find the zeros of a linear function, set the function equal to zero and solve for x. For example, for f(x) = 2x + 3, set 2x + 3 = 0 and solve for x.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.

Front

What is the significance of the slope in a linear function?

Back

The slope indicates the steepness and direction of the line. A positive slope means the line rises, while a negative slope means it falls.

Front

What does the y-intercept represent in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of the function when x = 0.

Front

How can you graph a linear function?

Back

To graph a linear function, identify the y-intercept, use the slope to find another point, and draw a straight line through these points.

Front

What is the relationship between the zeros of a function and its graph?

Back

The zeros of a function are the x-values where the graph intersects the x-axis. These points indicate where the function's value is zero.

Front

Can a linear function have more than one zero?

Back

No, a linear function can have at most one zero because it is represented by a straight line, which can intersect the x-axis at only one point.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.