# Exploring a function f(x) with absolute value

• Dell
In summary, an absolute value function is a mathematical function that returns the distance of a number from zero on a number line. To graph an absolute value function, identify the vertex point and plot points on either side to create a V-shaped curve. The domain is all real numbers and the range is limited to non-negative numbers. To solve an equation involving an absolute value function, isolate the expression and create two separate equations. An absolute value function can only have one vertex point as it changes direction at the vertex.
Dell
when i am exploring a function eg. f(x)=|2x-6|

can i treat it as two separate function all the way through, one to the left of x=3 and one to the right, and only at the very end, when i draw the graph connect them, ie draw a graph according to all the values i found from each side? will this work whenever i have absolute value of a basic polynom, should this always come out as a mirror image?

Dell said:
when i am exploring a function eg. f(x)=|2x-6|

can i treat it as two separate function all the way through, one to the left of x=3 and one to the right, and only at the very end, when i draw the graph connect them, ie draw a graph according to all the values i found from each side?
Yes. You won't have to connect them at the end, since the two halves will already be connected at x = 3.
Dell said:
will this work whenever i have absolute value of a basic polynom, should this always come out as a mirror image?
Yes, if you mean the mirror image across the x-axis. Take for example the function g(x) = |x^2 - 2x|. For x < 0 or x > 2, the graph looks exactly like that of the parabola y = x^2 - 2x. However, for 0 < x < 2, the portion of the graph of the parabola that lies below the x-axis is relected across it.

## 1. What is an absolute value function?

An absolute value function is a mathematical function that returns the distance of a number from zero on a number line. It always returns a positive value, regardless of the input.

## 2. How do I graph an absolute value function?

To graph an absolute value function, first identify the vertex point, which is the point where the function changes direction. Then, plot points on either side of the vertex to create a V-shaped curve. Finally, connect the points to create the graph.

## 3. What is the domain and range of an absolute value function?

The domain of an absolute value function is all real numbers, as it can take any input. The range, however, is limited to non-negative numbers as the function always returns a positive value.

## 4. How do I solve an equation involving an absolute value function?

To solve an equation involving an absolute value function, you must isolate the absolute value expression and then create two separate equations, one with a positive value and one with a negative value. Solve both equations to find all possible solutions.

## 5. Can an absolute value function have more than one vertex point?

No, an absolute value function can only have one vertex point. This is because the function changes direction at the vertex, and any additional vertex points would result in multiple changes in direction, which is not possible for an absolute value function.

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