Question

Identify the x and y intercepts of the graph of the function below. Type your intercepts as a point (x,y). If an intercept does not exist type "none". If more than one intercept exists you can type either intercept.f(x)= 4|x-3|+4 x intercept = Answery intercept = Answer

Answer 1

y-intercept = (0, 16)

x-intercept = none

Step-by-step explanation:

Given the below function;

`f(x)=4|x-3|+4`

To be able to graph the above function, let's choose values of x and determine the corresponding values of fx);

When x = -1;

`\begin{gathered} f(-1)=4|-1-3|+4 \\ =4|-4|+4 \\ =4\cdot4+4 \\ =16+4 \\ =20 \end{gathered}`

When x = 0;

`\begin{gathered} f(0)=4|0-3|+4 \\ =4\cdot3+4 \\ =12+4 \\ =16 \end{gathered}`

When x = 3;

`\begin{gathered} f(3)=4|3-3|+4 \\ =4\cdot0+4 \\ =4 \end{gathered}`

Wen x = 6;

`\begin{gathered} f(6)=4|6-3|+4 \\ =4\cdot3+4 \\ =12+4 \\ =16 \end{gathered}`

See below the graph of the given function;

The y-intercept of a graph is the point where the graph crosses the y-axis. In the above graph, we can see that the graph crosses the y-axis at x = 0 and y = 16, therefore its y-intercept is (0, 16)

The x-intercept of a graph is where the graph crosses the x-axis. We can see from the above graph that the graph does not cross the x-axis, therefore the x-intercept does not exist.