Question

Express the function graphed on the axes below as a piecewise function.

please help i don’t know what i’m doing.

Answer 1

The function graphed on the axes as a piecewise function is
`f(x)=\left\{\begin{array}{Ir}-2x+4, & \text{if } x > 0\\-2x + 4 ,& \text{if } x < 0\\-1, & \text{if } x = 3\end{array}\right`

In Mathematics and Euclidean Geometry, the intercept form of the equation of a standard line can be modeled by the following formula;

x/a + y/b = 1

Where:

a and b are x-intercept and y-intercept respectively.

Since the graph of this function has an x-intercept of (2, 0) and a y-intercept of (0, 4), an equation that represents the line can be written as follows;

x/2 + y/4 = 1

(2x + y)/4 = 1

By cross-multiplying, we have the following;

2x + y = 4

y = -2x + 4

f(x) = -2x + 4, if x > 0

f(x) = -2x + 4, if x < 0

Since there is a solid dot above the point (3, -2), a function to model the situation can be written as follows;

f(x) = -1, if x = 3.

Therefore, the piecewise function can be written as follows;

`f(x)=\left\{\begin{array}{Ir}-2x+4, & \text{if } x > 0\\-2x + 4 ,& \text{if } x < 0\\-1, & \text{if } x = 3\end{array}\right`