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-intercept of the graph of the function.

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 of a linear function?

Back

The slope of a linear function is a measure of its steepness, represented by 'm' in the equation f(x) = mx + b. It is calculated as the change in y divided by the change in x.

Front

What is the y-intercept of a linear function?

Back

The y-intercept of a linear function is the point where the graph intersects the y-axis. It is represented by 'b' in the equation f(x) = mx + b.

Front

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

Back

The slope indicates the direction and rate of change of the function. A positive slope means the function is increasing, while a negative slope means it is decreasing.

Front

What does it mean if a linear function has a slope of zero?

Back

If a linear function has a slope of zero, it means the function is constant and the graph is a horizontal line.

Front

How can you graph a linear function?

Back

To graph a linear function, identify the y-intercept (b) on the y-axis, use the slope (m) 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 correspond to the x-intercepts of its graph, where the graph crosses the x-axis.

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.