Question

Which is an x-intercept of the continuous function in the table?

(–1, 0)
(0, –6)
(–6, 0)
(0, –1)

Answer 1

we know that

The x-intercept is the value of the variable x when the value of the function is equal to zero

so

In the table we have

$(-1, 0)$ is a x-intercept, because

For $x=-1$ the value of the function is equal to zero

$(-6, 0)$ is a x-intercept, because

For $x=-6$ the value of the function is equal to zero

therefore

the answer is

the continuous function in the table has two x-intercepts

$(-1, 0)$

$(-6, 0)$

Answer 2

A x-intercept of the continuous function in the table is (–1, 0) and (–6, 0)

Further explanation

Straight-line equations are mathematical equations that are described in the plane of cartesian coordinates

A linear equation is an equation with 2 variables

General formula

y-y1 = m (x-x1)

or

y = mx + c

Where

m = straight-line gradient which is the slope of the line

x1, y1 = the Cartesian coordinate that is crossed by the line

c = constant m = Δy / Δx

The formula for a gradient (m) between 2 points in a line

m = Δy / Δx

$\large{\boxed{\bold{m=\frac{y_2-y_1}{x_2-x_1}}}$

Straight line equation, can be stated in:

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

The graph of this equation is a line

It takes at least 2 points to draw a graph of the line equation in the coordinate plane

A discrete function consists of points that have been determined

If we extend the line in both directions we will get a continuous function

The x-intercept: the point in which a line equation crosses the x-axis (the value of x when y = 0, (x, 0))

The y-intercept: the point in which a line equation crosses the y-axis (the value of y when x = 0, (0, y))

To find the correct x-intercept for the continuous function of the answer choices above, is to select a pair of points that have the value y = 0, i.e. point (–1, 0) and (–6, 0)

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Keywords: x-intercept,the continuous function