Question

Need assistance in solving the picture.

Answer 1

The equation of the function shown in the graph above is
`f(x) < \left\{\begin{array}{Ir}-x+7, & \text{if } x < -2\\x-3 ,& \text{if } x > -2\end{array}\right`

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

`y - y_1 = m(x - x_1)`

Where:

• x and y represent the data points.
• m represent the slope.

First of all, we would determine the slope of the downward sloping line by using these points (-7, 0) and (-8, 1);

Slope (m) = (1 - 0)/(-8 + 7)

Slope (m) = -1

At data point (-7, 0) and a slope of -1, a function for this line can be calculated by using the point-slope form as follows:

y - 0 = -1(x + 7)

y = -x - 7

f(x) < -x - 7, if x < -2.

For the upward sloping line, we have;

Slope (m) = (3 - 0)/(0 + 3)

Slope (m) = 1

At data point (3, 0) and a slope of 1, a function for this line can be calculated by using the point-slope form as follows:

y - 0 = 1(x - 3)

y = x - 3

f(x) < x - 3, if x > -2.

Therefore, the piecewise function can be written as follows;

`f(x) < \left\{\begin{array}{Ir}-x+7, & \text{if } x < -2\\x-3 ,& \text{if } x > -2\end{array}\right`