Question

How do u get the range of a function for example in question 8 explain the range for like a and f

Answer 1

Explanation:

We are to sketch the graph of the function and also state the intercepts, range, and domain of the function

Question 8a

`y=|x^2-4|`

To answer the question

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.

The domain of a function is the complete set of possible values of the independent variable

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain

For the question, we will have to plot the graph which is shown below

From the above

`\mathrm{X\:Intercepts}:\:\left(-2,\:0\right),\:\left(2,\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:4\right)`

From the graph, we can observe the value of y ranges from 0 to positive infinity. therefore, we can represent this as:

`\begin{gathered} Range \\ \\ \begin{bmatrix}\mathrm{Solution:}\: & \:y\ge\:0\: \\ \:\mathrm{Interval\:Notation:} & \:[0,\:\infty\:)\end{bmatrix} \end{gathered}`

For the Domain, we can observe that the values of x span from negative infinity to positive infinity, therefore, we can represent this as:

The graph is shown below

`\mathrm{Y\:Intercepts}:\:\left(0,\:16\right)`