The quadratic function's table shows a decrease from X = 4 to X = 1. The graph of "g(x)" is a translation of "|x|," accurately represented by "g(x) = |x - 1| - 1." The statements about range and domain are correct.
1. For the quadratic function represented by the table, the interval of decrease can be identified by examining the values of Y corresponding to different X-values. From the given data, the interval of decrease occurs from X = 4 to X = 1, where the Y-values decrease from 16 to 1.
2. The graph of function g(x) is a transformation of the parent function f(x) = |x|, translated 1 unit right and 1 unit down. The peak of the broad V-shape is located at (1, -1), and it intersects the x-axis at (-1, 0) and (3, 0).
The translation is accurately described by the equation g(x) = |x - 1| - 1, indicating a shift of 1 unit to the right and 1 unit down from the parent function.
Regarding the statements:
- The range is correctly described as "y ≤ 1," considering the downward shift of 1 unit.
- The domain is accurately stated as "all real numbers."
- The given equation "g(x) = |x + 1| - 1" represents a translation of the parent function, but it's not consistent with the described transformation.
In summary, the graph of "g(x)" is a translation of "f(x) = |x|" with the correct equation "g(x) = |x - 1| - 1," and the statements about range and domain are accurate.
The question probable may be:
1. Consider the quadratic function represented by the table. Identify the interval of decrease. The values of X and Y are given as follows:
X: -4, -3, -2, -1, 0, 1, 2, 3, 4
Y: 16, 9, 4, 1, 0, 1, 4, 9, 16
2. The graph of function g(x) is shown below. select all the true statements.
The graph is like a broad v shape whose peak is it coordinate ( 1 , -1) and then passes hru x axis at ( -1 , 0) and( 3 , 0)
was translated 1 unit right and 1 unit down from its parent function f(x) = |x|
can be represented by the equation g(x) = |x - 1| - 1
range y ≤ 1
domain: all real numbers
can be represented by the equation g(x) = | x+1 | - 1