Question

Complete the rule for g(x) so that the graph represents itThere are 5 blank spaces that need to be answered/filled

Answer 1

Based on the graph, the rule for g(x) should be completed as follows;
`gf(x)=\left\{\begin{array}{Ir}-10, \;-15\leq x < -10\\-8,\; -10\leq x < -8\\-6, \;-8\leq x < -1\\2, \;-1\leq x < 1\\4, \;1\leq x < 10\\8, \;10\leq x < 15\end{array}\right`

In Mathematics and Euclidean Geometry, a piecewise-defined function is a type of function that is defined by two or more mathematical expressions over a specific domain.

Note: The inequality symbol < or > represents a hollow dot (circle).

The inequality symbol ≤ or ≥ represents a solid dot (circle).

Generally speaking, the domain of any piecewise-defined function is the union of all of its sub-domains. By critically observing the given piecewise-defined function, we have the following domains;

Domain = -15 ≤ x < -10, for g(x) = -10.

Domain = -10 ≤ x < 8, for g(x) = -8.

Domain = -8 ≤ x < -1, for g(x) = -6

Domain = -1 ≤ x < 1, for g(x) = 2

Domain = 1 ≤ x < 10, for g(x) = 4

Domain = 10 ≤ x < 15, for g(x) = 8

In this context, the piecewise function for g(x) can be written as follows;

`gf(x)=\left\{\begin{array}{Ir}-10, \;-15\leq x < -10\\-8,\; -10\leq x < -8\\-6, \;-8\leq x < -1\\2, \;-1\leq x < 1\\4, \;1\leq x < 10\\8, \;10\leq x < 15\end{array}\right`

Answer 2

Answer:

Explanations:

The task is to look for the value of g(x), that is, y for all the given ranges of the values of x.

By looking closely at the graph, the complete rule for g(x) is shown below:

`f(x)=\begin{cases}-10\text{ -15} \\ \square \\ \square\end{cases}`