Which is a y-intercept of the continuous function in the table? (0, –6) (–2, 0) (–6, 0) (0, –2)

The y-intercept corresponding to the continuous function in the table is (0, –6).

Explanation

Linear equations refer to mathematical formulas represented in the plane of Cartesian coordinates.

A linear equation involves two variables.

Commonly used formulas include:

y-y1 = m (x-x1)

or

y = mx + c

Where:

m denotes the slope of the line

and x1, y1 are the intersecting Cartesian coordinates of the line

and c is the constant.

Moreover, the slope (m) can be derived between two points on a line:

m = Δy / Δx

In the linear equation context, it can also be expressed as:

• y = mx
• ax + by = ab
• y = a
• x = a
• etc.

The representation of this equation yields a straight line.

To sketch a graph of a linear equation within the coordinate plane, at least 2 points are required.

A discrete function comprises defined points.

By extending the line in both directions, we conceive a continuous function.

The x-intercept: denotes the point where a line intersects the x-axis (the value of x when y = 0, (x, 0)).

The y-intercept: denotes the point where a line crosses the y-axis (the value of y when x = 0, (0, y)).

We complete the answer choices not already accounted for in the example above.

There are four points identified for selecting the y-intercept, which are (-4, -10),

(-3.0), (-2.0), (-1, -4), (0, -6), (1,0).

To identify the correct y-intercept for the continuous function among the given selections, we must opt for a point where the x-value is 0, specifically point (0, -6).

Additional Resources

F (x) = x² + 1 g (x) = 5 - x

Link:

The inverse function f (x) = 2x-10

Link:

Exploring the function's domain

Link:

Keywords: y-intercept, the continuous function

The y-intercept is the location where any graph meets the y-axis.

Conversely, the x-intercept is where a graph intersects the x-axis.

This indicates that the coordinates at the intercept will always have the x-value as 0. Therefore, points of the format (0, y) represent y-intercepts, while points in the format (x, 0) indicate x-intercepts.

The provided points are:

(0,-6): y-intercept

(-2,0): x-intercept

(-6,0): x-intercept

(0,-2): y-intercept