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The graph of the absolute value parent function, ( f(x) = |x| ), has a V-shape with its vertex at the origin (0, 0). It is symmetric about the y-axis, indicating that it is an even function. The graph consists of two linear segments that extend infinitely in the positive y-direction, with a slope of 1 for ( x \geq 0 ) and a slope of -1 for ( x < 0 ). Additionally, it never dips below the x-axis, as absolute values are always non-negative.

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If you apply the changes below to the absolute value parent function F(x) x what is the equation of the new function Shift 8 units left. Shift 3 units Dow?

To shift the absolute value parent function ( F(x) = |x| ) eight units to the left, you replace ( x ) with ( x + 8 ), resulting in ( F(x) = |x + 8| ). Then, to shift the function down three units, you subtract 3 from the entire function, yielding the final equation ( F(x) = |x + 8| - 3 ).


What is composite function?

This is a combination of two functions, where you apply the first function and get a result and then fill that answer into the second function. OR These are what you get when you take the output of one function and use it to solve the output of the next function.


What do you do when subtracting absolute value integers?

When subtracting absolute value integers, first calculate the absolute values of the integers involved. Then, perform the subtraction using the absolute values. Remember that the result will always be a non-negative integer, as absolute values are always positive or zero. If necessary, apply the appropriate sign based on the original integers' values after the subtraction.


What is the range of absolute value functions My teacher said it would be all real numbers. However I thought it would be positive real numbers. Can you explain who is right and why?

The absolute value of a number is positive, so the range is always a positive real number. You are correct. The domain, that is the value before you take the absolute value, is all real numbers, but the range is always positive.


What is an inverse of a function?

The opposite of another function - if you apply a function and then its inverse, you should get the original number back. For example, the inverse of squaring a positive number is taking the square root.

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