Absolute Value - Algebra 2

First isolate the absolute value.

The two possible values for 2-3x are 5 and -5.

or

or

First isolate the absolute value:

There are two possible values for : 7 and -7.

or

or

First isolate the absolute value.

The two possible values for 2-3x are 5 and -5.

or

or

First isolate the absolute value.

There are no real numbers for which you can take the absolute value and get a negative number. Therefore, there are no values for x that will satisfy the equation.

First isolate the absolute value.

There are no real numbers for which you can take the absolute value and get a negative number. Therefore, there are no values for x that will satisfy the equation.

First isolate the absolute value:

There are two possible values for : 7 and -7.

or

or

First isolate the absolute value.

There are no real numbers for which you can take the absolute value and get a negative number. Therefore, there are no values for x that will satisfy the equation.

First isolate the absolute value.

The two possible values for 2-3x are 5 and -5.

or

or

First isolate the absolute value:

There are two possible values for : 7 and -7.

or

or

First isolate the absolute value.

There are no real numbers for which you can take the absolute value and get a negative number. Therefore, there are no values for x that will satisfy the equation.

First isolate the absolute value.

The two possible values for 2-3x are 5 and -5.

or

or

We start by finding the midpoint of the interval, which is enclosed by 60% of 204 and 80% of 204.

We find the midpoint, or average, of these endpoints by adding them and dividing by two:

142.5 is exactly 20.5 units away from both endpoints, 122 and 163. Since we are looking for the range of numbers between 122 and 163, all possible values have to be within 20.5 units of 142.5. If a number is greater than 20.5 units away from 142.5, either in the positive or negative direction, it will be outside of the \[122, 163\] interval. We can express this using absolute value in the following way:

The formula of an absolute value function is where m is the slope, a is the horizontal shift and b is the vertical shift. The slope can be found with any two adjacent integer points, e.g. and , and plugging them into the slope formula, , yielding . The vertical and horizontal shifts are determined by where the crux of the absolute value function is. In this case, at , and those are your a and b, respectively.

Below is the graph of :

The given graph is the graph of translated by moving the graph 7 units left (that is, unit right) and 2 units down (that is, units up)

The function graphed is therefore

where . That is,

Below is the graph of :

The given graph is the graph of reflected in the -axis, then translated left 2 units (or, equivalently, right units. This graph is

, where .

The function graphed is therefore

Below is the graph of :

The given graph is the graph of reflected in the -axis, then translated up 6 units. This graph is

, where .

The function graphed is therefore

The equation can be determined from the graph by following the rules of transformations; the base equation is:

The graph of this base equation is:

When we compare our graph to the base equation graph, we see that it has been shifted right 3 units, up 1 unit, and our graph has been stretched vertically by a factor of 2. Following the rules of transformations, the equation for our graph is written as:

Let

The graph of this basic absolute value function is a "V"-shaped graph with a vertex at the origin, or the point with coordinates . In terms of ,

The graph of this function can be formed by shifting the graph of left 6 units ( ) and down 7 units (). The vertex is therefore located at .

Let

The graph of this basic absolute value function is a "V"-shaped graph with a vertex at the origin, or the point with coordinates . In terms of ,

,

or, alternatively written,

The graph of is the same as that of , after it shifts 10 units left ( ), it flips vertically (negative symbol), and it shifts up 10 units (the second ). The flip does not affect the position of the vertex, but the shifts do; the vertex of the graph of is at .