Write an equation involving absolute value for the graph

Question

An absolute value function is a function that contains an algebraic expression within absolute value symbols. Recall that the absolute value of a number is its distance from 0 on the number line.

Table of Contents Show

Vertical Shift
Horizontal Shift
Stretch and Compression
1 Expert Answer
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How do you find the equation of an absolute value equation?

The absolute value parent function, written as f(x)=|x|, is defined as

f(x)={x if x>00 if x=0−x if x<0

To graph an absolute value function, choose several values of x and find some ordered pairs.

x	y=\|x\|
−2	2
−1	1
0	0
1	1
2	2

Plot the points on a coordinate plane and connect them.

Observe that the graph is V-shaped.

(1) The vertex of the graph is (0,0).

(2) The axis of symmetry (x=0 or y-axis) is the line that divides the graph into two congruent halves.

(3) The domain is the set of all real numbers.

(4) The range is the set of all real numbers greater than or equal to 0. That is, y ≥0.

(5) The x-intercept and the y-intercept are both 0.

Vertical Shift

To translate the absolute value function f(x )=|x| vertically, you can use the function

g(x)=f(x)+k.

When k>0, the graph of g(x) translated k units up.

When k<0, the graph of g(x) translated k units down.

Horizontal Shift

To translate the absolute value function f(x)=|x| horizontally, you can use the function

g(x)=f(x−h).

When h>0, the graph of f(x) is translated h units to the right to get g(x).

When h<0, the graph of f(x) is translated h units to the left to get g(x ).

Stretch and Compression

The stretching or compressing of the absolute value function y=|x| is defined by the function y=a|x| where a is a constant. The graph opens up if a>0 and opens down when a<0.

For absolute value equations multiplied by a constant (for example,y=a| x|),if 0<a<1, then the graph is compressed, and if a>1, it is stretched. Also, if a is negative, then the graph opens downward, instead of upwards as usual.

More generally, the form of the equation for an absolute value function is y=a|x−h|+k. Also:

The vertex of the graph is (h,k).
The domain of the graph is set of all real numbers and the range is y≥k when a>0.
The domain of the graph is set of all real numbers and the range is y≤k when a<0.
The axis of symmetry is x=h.
It opens up if a>0 and opens down if a<0.
The graph y=| x| can be translated h units horizontally and k units vertically to get the graph of y=a|x−h|+k.
The graph y=a|x| is wider than the graph of y=|x| if |a|<1 and narrower if |a|>1.

Hime K.

asked • 09/02/21

On the graph from left to right it: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5. The dots are put on 3 and 5.

1 Expert Answer

I don't know if this is exactly what you're asking, but it sounds like you need to create an equation where the solution is the set 3 and 5. If you find the number just between the two values and the distance from the center, the problem is easy. Just use |x-c|=r Where c is the center and r is the distance. The average gives you the number between, whuch here is just adding and then dividing by two. 3+5=8 8/2=4 so r=4 is the average. the distance from 4 to 5 is r=1 so |x-4|=1 is the equation. You can check by plugging in 3 and 5 to the x in the equation.

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How do you find the equation of an absolute value equation?

To solve an equation containing absolute value, isolate the absolute value on one side of the equation. Then set its contents equal to both the positive and negative value of the number on the other side of the equation and solve both equations. Solve | x | + 2 = 5.

write equation involving absolute graph